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 - Bridge of Knowledge

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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)].

Description

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

Dataset file

MaximumNormErrors[0,gamma]Solution.zip
5.4 kB, S3 ETag 3ab79e264c9b332094931bd5fa7e14d4-1, downloads: 15
The file hash is calculated from the formula
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.

Example script for calculation:
https://github.com/antespi/s3md5
download file MaximumNormErrors[0,gamma]Solution.zip

File details

License:
Creative Commons: by 4.0 open in new tab
CC BY
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Details

Year of publication:
2020
Verification date:
2020-12-17
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
DOI:
DOI ID 10.34808/qrg1-g425 open in new tab
Verified by:
Gdańsk University of Technology

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