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Wyniki wyszukiwania dla: ORDINARY DIFFERENTIAL EQUATION
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Ordinary differential equations with deviated arguments
PublikacjaPraca dotyczy istnienia i przybliżonych rozwiązań dla problemów brzegowych z opóźnionymi oraz wyprzedzonymi argumentami. Dyskutowano też pewne nierówności różniczkowe powyższego typu.
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First-order impulsive ordinary differential equations with advanced arguments
PublikacjaPraca dotyczy problemów istnienia rozwiązań dla równań różniczkowych z impulsami i nieliniowymi warunkami brzegowymi. Są to równania z argumentami wyprzedzonymi. Podano warunki dostateczne na istnienie rozwiązań. W pracy są również dyskutowane nierówności różniczkowe z impulsami. Podano też przykłady ilustrujące otrzymane wyniki.
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Boundary value problems for ordinary differential equations with deviated arguments
PublikacjaDyskutowane są równania różniczkowe z dwupunktowym nieliniowym warunkiem brzegowym z argumentami typu odchylonego. Podano warunki dostateczne które gwarantują iż problem wyjściowy ma kwazi-rozwiązania. Podano też warunki przy których problem ten ma rozwiązanie. Wyniki uzyskano stosując metodę iteracji monotonicznych.Badano też pewne nierówności różniczkowe z odchylonymi argumentami.
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Ordinary differential equations with nonlinear boundary conditions of antiperiodic type.
PublikacjaZastosowano metodę kwazilinearyzacji do równań różniczkowych zwyczajnych z nieliniowymi warunkami brzegowymi typu antyokresowego. Podano warunki dostateczne przy których iteracje monotoniczne są zbieżne do jedynego rozwiązania naszego problemu i jest to zbieżność kwadratowa. Iteracje te są rozwiązaniami odpowiednich równań liniowych z liniowymi warunkami brzegowymi.
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Linear boundary problems for ordinary differential equations with deviated arguments
PublikacjaPraca dotyczy istnienia i jednoznaczności rozwiązań dla problemów brzegowych w tym również i problemów z wielopunktowymi warunkami brzegowymi.
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Boundary value problems for first-order impulsive ordinary differential equations with delay arguments
PublikacjaPraca dotyczy problemów istnienia rozwiązań dla pierwszego rzędu równań różniczkowych typu opóźnionego z impulsami. Podano warunki dostateczne na istnienie ekstremalnych kwazi-rozwiązań. Podano też warunki przy których powyższe zagadnienie ma jedyne rozwiązanie. Praca zawiera też przykład ilustrujący otrzymane wyniki teoretyczne.
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A comparison method for ordinary differential systems
PublikacjaPraca dotyczy problemów istnienia i jednoznaczności rozwiązań oraz ciągłej zależności dla układów równań różniczkowych w tym i z opóźnionymi argumentami z warunkami początkowymi oraz brzegowymi typu okresowego. Przy odpowiednich założeniach, stosując teorię nierówności różniczkowych, pokazano, że odpowiednia funkcja porównawcza może być ujemna, co ma istotne znaczenie w dalszych badaniach. Pokazano, że konstruowany ciąg iteracji...
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Computational issues of solving the 1D steady gradually varied flow equation
PublikacjaIn this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution....
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Different types of solvability conditions for differential operators
PublikacjaSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublikacjaIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Inverse Flood Routing Using Simplified Flow Equations
PublikacjaThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials
PublikacjaNanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the...
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PROPERTIES OF ONE DIMENSIONAL OPEN-CHANNEL STEADY FLOW EQUATIONS
PublikacjaIn this paper properties of discrete forms of one dimensional steady gradually varied flow equations are discussed. Such forms of flow equations are obtained as a result of approximation of their differential forms, which is required to solve them numerically. For such purpose explicit or implicit numerical approximation schemes for ordinary differential equations can be applied. It turns out that dependently on the chosen approximation...
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Subcritical bifurcation of free elastic shell of biological cluster
PublikacjaIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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An inclination in Thermal Energy Using Nanoparticles with Casson Liquid Past an Expanding Porous Surface
PublikacjaPhysical aspects of inclined MHD nanofluid towards a stretching sheet embedded in a porous medium are visualized. Two types of nanoparticles are used named as copper and alumna dioxide with water as base fluid. Similarity transformations are used to convert the partial differential equations into the set of ordinary differential equation. Closed solutions are found to examine the velocity and the temperature profiles. It is examined...
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Numerical Analysis of Steady Gradually Varied Flow in Open Channel Networks with Hydraulic Structures
PublikacjaIn this paper, a method for numerical analysis of steady gradually varied fl ow in channel networks with hydraulic structures is considered. For this purpose, a boundary problem for the system of ordinary differential equations consisting of energy equation and mass conservation equations is formulated. The boundary problem is solved using fi nite difference technique which leads to the system of non-linear algebraic equations....
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Modelling the malware propagation in mobile computer devices
PublikacjaNowadays malware is a major threat to the security of cyber activities. The rapid develop- ment of the Internet and the progressive implementation of the Internet of Things (IoT) increase the security needs of networks. This research presents a theoretical model of malware propagation for mobile computer devices. It is based on the susceptible-exposed- infected-recovered-susceptible (SEIRS) epidemic model. The scheme is based on...
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Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance
PublikacjaThe impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Dane BadawczeThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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A solution of non-linear differential problem with application to selected geotechnical problems
PublikacjaA certain non-linear differential equation containing a power of unknown function being the solution is considered with application to selected geotechnical problems. The equation can be derived to a linear differential equation by a proper substitution and properties of the operations G and S.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Dane BadawczeThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Dane BadawczePresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Method of lines for Hamilton-Jacobi functional differential equations.
PublikacjaInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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Method of lines for physiologically structured models with diffusion
PublikacjaWe deal with a size-structured model with diffusion. Partial differential equations are approximated by a large system of ordinary differential equations. Due to a maximum principle for this approximation method its solutions preserve positivity and boundedness. We formulate theorems on stability of the method of lines and provide suitable numerical experiments.
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Karolina Lademann mgr
OsobyCurriculum vitae
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Equations with Separated Variables on Time Scales
PublikacjaWe show that the well-known theory for classical ordinary differential equations with separated variables is not valid in case of equations on time scales. Namely, the uniqueness of solutions does not depend on the convergence of appropriate integrals.
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublikacjaThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublikacjaAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublikacjaIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublikacjaThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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Towards a classification of networks with asymmetric inputs
PublikacjaCoupled cell systems associated with a coupled cell network are determined by (smooth) vector fields that are consistent with the network structure. Here, we follow the formalisms of Stewart et al (2003 SIAM J. Appl. Dyn. Syst. 2, 609–646), Golubitsky et al (2005 SIAM J. Appl. Dyn. Syst. 4, 78–100) and Field (2004 Dyn. Syst. 19, 217–243). It is known that two non-isomorphic n-cell coupled networks can determine the same sets of...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublikacjaDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Crystallization kinetics study of dynamically vulcanized PA6/NBR/HNTs nanocomposites by nonisothermal differential scanning calorimetry
PublikacjaInvestigation of crystallization behavior and kinetics of thermoplastic elastomer nanocomposites was the subject of limited works because of complexities associated with semiexperimental modeling of such phenomenon in a system containing components having completely different behavior in the molten state. Nonisothermal crystallization kinetics of dynamically vulcanized PA6/NBR/HNTs thermoplastic elastomer nanocomposites was mathematically...
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Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublikacjaIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Parameter and delay estimation of linear continuous-time systems
PublikacjaIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous identification...
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Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow
PublikacjaTo find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and...
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Analysis of a gene expression model
PublikacjaWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the number of active binding sites, the way in which dimers bind to DNA and time delay in translation process. For a simplified model that consist of three ordinary differential equations with time delay we derive conditions for stability of the positive steady state and for the...
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Parameter and delay estimation of linear continuous-time systems
PublikacjaIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is usually described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous...
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On–line Parameter and Delay Estimation of Continuous–Time Dynamic Systems
PublikacjaThe problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous...
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On local buckling of cold-formed channel members
PublikacjaThe paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy...
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A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect
PublikacjaThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations...
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Torsional buckling and post-buckling of columns made of aluminium alloy
PublikacjaThe paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation...
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublikacjaThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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Application of muscle model to the musculoskeletal modeling
PublikacjaThe purpose of this paper is to investigate new fusiform muscle models. Each of these models treats a muscle as a system composedof parts characterized by different mechanical properties. These models explain the influence of differences in the stiffness of lateral parts and the degree of muscle model discretization. Each muscle model is described by a system of differential equations and a single integro-differential equation....
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The finite difference methods of computation of X-rays propagation through a system of many lenses
PublikacjaThe propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric The propagation of X-ray waves through an optical system...
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublikacjaThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
PublikacjaIn this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodalmap. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily...
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Introduction to Numerical Simulation
Kursy OnlineCourse description: This interdisciplinary course provides an introduction to computational techniques for the simulation of a broad range of engineering and physical systems. Concepts and methods discussed are widely illustrated by applications drawn from electrical, mechanical, and chemical engineering. Topics include: mathematical formulations of simulation problems; sparse direct and iterative linear system solution techniques,...