Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems
Abstract Objective The main purpose of this work is to present a fourth-order fitted mesh scheme for solving the semilinear singularly perturbed reaction–diffusion problem to produce more accurate solutions. Results Quasilinearization technique is used to linearize the semilinear term. The scheme is...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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BMC
2023-11-01
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| Series: | BMC Research Notes |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13104-023-06631-5 |
| _version_ | 1827604438245703680 |
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| author | Birtukan Tebabal Reda Tesfaye Aga Bullo Gemechis File Duressa |
| author_facet | Birtukan Tebabal Reda Tesfaye Aga Bullo Gemechis File Duressa |
| author_sort | Birtukan Tebabal Reda |
| collection | DOAJ |
| description | Abstract Objective The main purpose of this work is to present a fourth-order fitted mesh scheme for solving the semilinear singularly perturbed reaction–diffusion problem to produce more accurate solutions. Results Quasilinearization technique is used to linearize the semilinear term. The scheme is formulated with discretizing the solution domain piecewise uniformly and then replacing the differential equation by finite difference approximations. This gives the system of difference algebraic equations and is solved by the Thomas algorithm. Convergence analysis are investigated using solution bound and the truncation error bound. Numerical illustrations are investigated to support the theoretical results and the method’s applicability. The method produces a more accurate solution than some existing methods in the literature. |
| first_indexed | 2024-03-09T06:00:00Z |
| format | Article |
| id | doaj.art-3000e6ad1adc4052be3ebfd9efc3e089 |
| institution | Directory Open Access Journal |
| issn | 1756-0500 |
| language | English |
| last_indexed | 2024-03-09T06:00:00Z |
| publishDate | 2023-11-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Research Notes |
| spelling | doaj.art-3000e6ad1adc4052be3ebfd9efc3e0892023-12-03T12:09:26ZengBMCBMC Research Notes1756-05002023-11-011611910.1186/s13104-023-06631-5Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problemsBirtukan Tebabal Reda0Tesfaye Aga Bullo1Gemechis File Duressa2Department of Mathematics, College of Natural Science, Jimma UniversityDepartment of Mathematics, College of Natural Science, Jimma UniversityDepartment of Mathematics, College of Natural Science, Jimma UniversityAbstract Objective The main purpose of this work is to present a fourth-order fitted mesh scheme for solving the semilinear singularly perturbed reaction–diffusion problem to produce more accurate solutions. Results Quasilinearization technique is used to linearize the semilinear term. The scheme is formulated with discretizing the solution domain piecewise uniformly and then replacing the differential equation by finite difference approximations. This gives the system of difference algebraic equations and is solved by the Thomas algorithm. Convergence analysis are investigated using solution bound and the truncation error bound. Numerical illustrations are investigated to support the theoretical results and the method’s applicability. The method produces a more accurate solution than some existing methods in the literature.https://doi.org/10.1186/s13104-023-06631-5Semilinear singularly perturbedFourth-orderNon-uniform meshAccurate solution |
| spellingShingle | Birtukan Tebabal Reda Tesfaye Aga Bullo Gemechis File Duressa Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems BMC Research Notes Semilinear singularly perturbed Fourth-order Non-uniform mesh Accurate solution |
| title | Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems |
| title_full | Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems |
| title_fullStr | Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems |
| title_full_unstemmed | Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems |
| title_short | Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems |
| title_sort | fourth order fitted mesh scheme for semilinear singularly perturbed reaction diffusion problems |
| topic | Semilinear singularly perturbed Fourth-order Non-uniform mesh Accurate solution |
| url | https://doi.org/10.1186/s13104-023-06631-5 |
| work_keys_str_mv | AT birtukantebabalreda fourthorderfittedmeshschemeforsemilinearsingularlyperturbedreactiondiffusionproblems AT tesfayeagabullo fourthorderfittedmeshschemeforsemilinearsingularlyperturbedreactiondiffusionproblems AT gemechisfileduressa fourthorderfittedmeshschemeforsemilinearsingularlyperturbedreactiondiffusionproblems |