Numerical treatment of singularly perturbed unsteady Burger-Huxley equation
This article deals with the numerical treatment of a singularly perturbed unsteady Burger-Huxley equation. The equation is linearized using the Newton-Raphson-Kantorovich approximation method. The resulting linear equation is discretized using the implicit Euler method and an exponential spline meth...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-01-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.1061245/full |
| _version_ | 1797961886445076480 |
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| author | Imiru Takele Daba Gemechis File Duressa |
| author_facet | Imiru Takele Daba Gemechis File Duressa |
| author_sort | Imiru Takele Daba |
| collection | DOAJ |
| description | This article deals with the numerical treatment of a singularly perturbed unsteady Burger-Huxley equation. The equation is linearized using the Newton-Raphson-Kantorovich approximation method. The resulting linear equation is discretized using the implicit Euler method and an exponential spline method for time and space variables, respectively. Richardson's extrapolation technique is employed to increase the accuracy in the temporal direction. The stability and uniform convergence of the proposed scheme are investigated. The scheme is shown uniformly convergent with the order of convergence O(τ + ℓ2) and O(τ2 + ℓ2) before and after Richardson extrapolation, respectively. Several test examples are considered to validate the applicability and efficiency of the scheme. It is observed that the proposed scheme provides more accurate results than the methods available in the literature. |
| first_indexed | 2024-04-11T01:04:50Z |
| format | Article |
| id | doaj.art-f562bbace4874c9f93ae585e410902a5 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-11T01:04:50Z |
| publishDate | 2023-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-f562bbace4874c9f93ae585e410902a52023-01-04T13:51:47ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872023-01-01810.3389/fams.2022.10612451061245Numerical treatment of singularly perturbed unsteady Burger-Huxley equationImiru Takele Daba0Gemechis File Duressa1Department of Mathematics, Dilla University, Dilla, EthiopiaDepartment of Mathematics, Jimma University, Jimma, EthiopiaThis article deals with the numerical treatment of a singularly perturbed unsteady Burger-Huxley equation. The equation is linearized using the Newton-Raphson-Kantorovich approximation method. The resulting linear equation is discretized using the implicit Euler method and an exponential spline method for time and space variables, respectively. Richardson's extrapolation technique is employed to increase the accuracy in the temporal direction. The stability and uniform convergence of the proposed scheme are investigated. The scheme is shown uniformly convergent with the order of convergence O(τ + ℓ2) and O(τ2 + ℓ2) before and after Richardson extrapolation, respectively. Several test examples are considered to validate the applicability and efficiency of the scheme. It is observed that the proposed scheme provides more accurate results than the methods available in the literature.https://www.frontiersin.org/articles/10.3389/fams.2022.1061245/fullsingular perturbation problemburger-huxley equationimplicit Euler methodexponential fitted operator methodRichardson extrapolation |
| spellingShingle | Imiru Takele Daba Gemechis File Duressa Numerical treatment of singularly perturbed unsteady Burger-Huxley equation Frontiers in Applied Mathematics and Statistics singular perturbation problem burger-huxley equation implicit Euler method exponential fitted operator method Richardson extrapolation |
| title | Numerical treatment of singularly perturbed unsteady Burger-Huxley equation |
| title_full | Numerical treatment of singularly perturbed unsteady Burger-Huxley equation |
| title_fullStr | Numerical treatment of singularly perturbed unsteady Burger-Huxley equation |
| title_full_unstemmed | Numerical treatment of singularly perturbed unsteady Burger-Huxley equation |
| title_short | Numerical treatment of singularly perturbed unsteady Burger-Huxley equation |
| title_sort | numerical treatment of singularly perturbed unsteady burger huxley equation |
| topic | singular perturbation problem burger-huxley equation implicit Euler method exponential fitted operator method Richardson extrapolation |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.1061245/full |
| work_keys_str_mv | AT imirutakeledaba numericaltreatmentofsingularlyperturbedunsteadyburgerhuxleyequation AT gemechisfileduressa numericaltreatmentofsingularlyperturbedunsteadyburgerhuxleyequation |