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)]. - Open Research Data - MOST Wiedzy

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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)].

Opis

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. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses travelling-wave solutions that are positive and bounded. Only a few travelling-wave solutions of such model are known in exact form, therefore, the construction of the numerical methods that preserve properties of the mathematical model are highly desirable.

The complete convergence analysis of the constructed nonstandard difference scheme is available in the paper: On the convergence of a finite-difference discretization a la Mickens of the generalized Burgers–Huxley equation (2014) Vol. 20, No. 10, 1444–1451, http://dx.doi.org/10.1080/10236198.2014.936319.

We provide nonstandard approximation of the travelling wave solution bounded within [0, γ^(1/p)]. The dataset consists of text files (.txt) with simulation results which contain the maximum-norm errors. Results are obtained for couple of sets of model parameters:  α, γ, p and the space interval [-20,20]. Time interval is set to be [0,20]. Each file contains six results for different combination of time and space steps which satisfy the convergence conditions derived in the above paper.

  1. α = 1, γ = 0.8, p = 2 – solution01.txt
  2. α = 1, γ = 0.6, p = 2 – solution02.txt
  3. α = 1, γ = 0.4, p = 2 – solution03.txt
  4. α = 1, γ = 0.8, p = 1 – solution04.txt
  5. α = 1, γ = 0.6, p = 1 – solution05.txt
  6. α = 1, γ = 0.4, p = 1 – solution06.txt
  7. α = 0.6, γ = 0.8, p = 2 – solution07.txt
  8. α = 0.6, γ = 0.6, p = 2 – solution08.txt
  9. α = 0.6, γ = 0.4, p = 2 – solution09.txt
  10. α = 0.6, γ = 0.8, p = 1 – solution10.txt
  11. α = 0.6, γ = 0.6, p = 1 – solution11.txt
  12. α = 0.6, γ = 0.4, p = 1 – solution12.txt

Plik z danymi badawczymi

MaximumNormErrors[0,gamma]Solution.zip
5.4 kB, S3 ETag 3ab79e264c9b332094931bd5fa7e14d4-1, pobrań: 71
Hash pliku liczony jest ze wzoru
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} gdzie pojedyncza część pliku jest wielkości 512 MB

Przykładowy skrypt do wyliczenia:
https://github.com/antespi/s3md5
pobierz plik MaximumNormErrors[0,gamma]Solution.zip

Informacje szczegółowe o pliku

Licencja:
Creative Commons: by 4.0 otwiera się w nowej karcie
CC BY
Uznanie autorstwa

Informacje szczegółowe

Rok publikacji:
2020
Data zatwierdzenia:
2020-12-17
Język danych badawczych:
angielski
Dyscypliny:
  • matematyka (Dziedzina nauk ścisłych i przyrodniczych)
DOI:
Identyfikator DOI 10.34808/qrg1-g425 otwiera się w nowej karcie
Weryfikacja:
Politechnika Gdańska

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