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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2021.9
- 수록면
- 591 - 612 (22page)
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초록· 키워드
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In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-difiusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for di erent values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.
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참고문헌 (23)
참고문헌 신청
E. B. Becker / 1981 / Finite Elements, An Introduction: Volume I / Printice-Hall Inc
M. Chandru / 2015 / A Hybrid Difference Scheme for a Second-Order Singularly Perturbed Reaction-Diffusion Problem with Non-smooth Data / International Journal of Applied and Computational Mathematics 1(1):87~100
C. Clavero / 2009 / A robust second-order numerical method for global solution and global normalized flux of singularly perturbed self-adjoint boundaryvalue problems / Int. J. Comput. Math 86(10-11):1731~1745
G. File / 2017 / Higher order compact finite difference method for singularly perturbed one dimensional reaction-diffusion problems / J. Nigerian Math. Soc 36(3):491~502
G. File / 2013 / Domain Decomposition Method for Solving Singular Perturbation Problems / International Journal of Applied Science and Engineering 11(4):433~448
M. Chandru / 2015 / A Hybrid Difference Scheme for a Second-Order Singularly Perturbed Reaction-Diffusion Problem with Non-smooth Data / International Journal of Applied and Computational Mathematics 1(1):87~100
C. Clavero / 2009 / A robust second-order numerical method for global solution and global normalized flux of singularly perturbed self-adjoint boundaryvalue problems / Int. J. Comput. Math 86(10-11):1731~1745
G. File / 2017 / Higher order compact finite difference method for singularly perturbed one dimensional reaction-diffusion problems / J. Nigerian Math. Soc 36(3):491~502
G. File / 2013 / Domain Decomposition Method for Solving Singular Perturbation Problems / International Journal of Applied Science and Engineering 11(4):433~448
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