Search results for: METHOD OF LINES
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Method of lines for physiologically structured models with diffusion
PublicationWe 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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Method of lines for Hamilton-Jacobi functional differential equations.
PublicationInitial 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 nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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Numerical method of lines for first order partial differential functional equations
PublicationUdowodniono zbieżność numerycznej metody prostych dla równań różniczkowofunkcyjnych o pochodnych cząstkowych pierwszego rzędu i ich rozwiązań klasycznych określonych na piramidzie Haara. Zastosowano metodę nierówności różniczkowych.
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Generalized method of lines for nonlinear first order partial differential equations
PublicationKlasyczne rozwiązania zagadnień początkowych oraz początkowo brzegowych są przybliżane za pomocą rozwiązań równań różniczkowo różnicowych. Skonstruowana jest metoda prostych polegająca na dyskretyzacji wyjściowego równania względem zmiennych przestrzennych. Przedstawiony w pracy schemat bazuje na metodzie linearyzacji dla zagadnień nieliniowych. W pracy zastosowano metodę quasilinearyzacji polegającą na zamianie nieliniowego równania...
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Numerical method of lines for first order partial differential equations with deviated variables
PublicationPraca traktuje o przybliżaniu rozwiązań klasycznych równańróżniczkowo-funkcyjnych cząstkowych pierwszego rzędu rozwiązaniamiukładów quasiliniowych równań różnicowych. Nowe podejście dorozwiązywania równań nieliniowych zawdzięczamy metodziequasilinearyzacji dla zagadnień początkowo - brzegowych z odchylonymargumentem. Dla przyrostów pochodnych funkcji danej zakładamy nieliniowe oszacowanie typu Perrona. Załączone są wyniki eksperymentów...
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The iterative method in search for the state of equilibrium in anchor lines.
PublicationPrzedstawiono iteracyjną metodę rozwiązywania równań równowagi lin kotwicznych. Metoda jest szczególnie łatwa do zaprogramowania obliczeń numerycznych, ponieważ w każdym kroku iteracyjnym wymaga jedynie obliczania całek oznaczonych znanych funkcji. Wynikiem obliczeń są wartości sił podłużnych w linie i jej kształt, który na skutek oddziaływania prądu oceanicznego na linę może być krzywą przestrzenną. Przytoczone przykłady...
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Structural reliability of overhead power lines by means of Monte Carlo Method and RSM
PublicationThe article discusses the issue of reliability assessment of overhead power lines by means of both Monte Carlo Method and Response Surface Method. The suspension tower OS24 ON150+10 is considered, as the weakest element of the line. A comparison is made between deterministic and probabilistic approaches to wind and icing loading. The PDFs for wind and icing loads are proposed. Reliability is assessed for both critical atmospheric...
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Comments on ''An innovative fast powerful method for tackling electromagnetic eigenvalue problems for multistrip transmission lines''
PublicationPraca stanowi komentarz do publikacji Casanuevy i Garcii dotyczącej techniki szybkiego obliczania charakterystyk dyspersyjnych falowodów z niejednorodnym wypełnieniem. Zwrócono uwagę na niepotrzebną komplikację zagadnienia poprzez zastosowanie techniki rozkładu na wartości szczególne.
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GTM Method of Structural Studies Lecture and Laboratory
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THE APPLICATION EFFECTS OF CONTINUOUS SATELLITE MEASUREMENTS OF RAILWAY LINES
PublicationThe paper presents results of satel lite surveying of the railway's rout es, which have been conducted just after starting in Poland (in 2008) the Active Geodesy Network ASG-EU POS. Afterwards it was possible to effectively utilize the GNSS survey ing results for the inventory of the (exploring) railways in service. Already at the beginning of 2009, the research team from Gdansk University of Technology and Naval Academy in Gdynia,...
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Simulation of Signal Propagation Along Fractional-Order Transmission Lines
PublicationIn this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the...
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Calculations of Short-Circuit Current Flows in Earth Wires of HV Lines
PublicationThis paper presents a method which enables calculating flows of short-circuit currents in earth wires of high voltage transmission lines, and its implementation in the form of a computer programme. The algorithm enables performing calculations for a double-fed line and starconnected lines (three terminal lines). The developed programme enables verifying dimensioning of earth wires in the context of their short-circuit thermal withstand...
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Design of power cable lines partially exposed to direct solar radiation – special aspects
PublicationPower cable lines are usually buried in the ground. However, in some cases, their ending sections are mounted along the supports of overhead lines. This leads to a situation where the cables are exposed to direct solar radiation and, consequentially, overheat. The paper presents the advanced computer modelling of power cables’ heating, considering their insolation as well as the effect of wind. The temperature and current-carrying...
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Computer-Aided Calculations of Earth Potential Rise in High Voltage Overhead Lines
PublicationHigh voltage overhead power lines with earth wires comprise towers made of conductive material. Some towers are in locations where people can be expected to be either for a long time or for a short time but very frequently. Evaluation of shock hazard near such towers requires calculation of line-to-earth short-circuit current, earth current and especially earth potential rise. Number of towers in high voltage power lines can exceed...
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Experimental Comparison of Straight Lines and Polynomial Interpolation Modeling Methods in Ship Evolutionary Trajectory Planning Problem
PublicationPaper presents the application of evolutionary algorithms and polynomial interpolation in ship evolutionary trajectory planning method and its comparison to classic approach, where trajectory is modeled by straight lines. Evolutionary algorithms are group of methods that allows\ to find a collision free trajectory in real time, while polynomial interpolation allows to model smooth trajectory, which keeps continuity of velocity...
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Modelling of MV and HV Cable Lines
PublicationOverhead and cable lines are fundamental elements of power systems. Participation of cable lines is smaller and their percentage decreases as voltage is increased. HV cable lines are often built with the use of cables which are composed of coaxial metallic sheaths. Such cables are also often used in MV networks. The sheath may operate in different confgurations. In the case of Polish MV network the sheaths are earthed at both ends....
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EFFICIENT LINE DETECTION METHOD BASED ON 2D CONVOLUTION FILTER
PublicationThe article proposes an efficient line detection method using a 2D convolution filter. The proposed method was compared with the Hough transform, the most popular method of straight lines detection. The developed method is suitable for local detection of straight lines with a slope from -45˚ to 45˚. Also, it can be used for curve detection which shape is approximated with the short straight sections. The new method is characterized...
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Resonance problems in UHV transmission lines
PublicationThe paper presents resonance phenomena observed in 400 kV transmission lines in the Polish power system. Two events are analysed, when shunt reactors used for reactive power compensation, caused overvoltages and overcurrent protection tripping as a result of resonance. An oscillographic fault recordings from protection devices are compared to time domain simulation results. The obtained simulation results match fault recordings,...
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Ferrite coupled slot lines circulator.
PublicationW oparciu o metodę rodzajów sprzężonych przeprowadzono analizę macierzy rozproszenia sekcji ferrytowych linii szczelinowych (FLS). W oparciu o uzyskane wyniki opracowano model cyrkulatora zaprojektowany w postaci kaskadowego połączenia sekcji FLS oraz szczelinowego rozgałęzienia typu T. Określono parametry rozproszenia układu, które zweryfikowano eksperymentalnie.