AN EFFICIENT PARAMETER UNIFORM SPLINE-BASED TECHNIQUE FOR SINGULARLY PERTURBED WEAKLY COUPLED REACTION-DIFFUSION SYSTEMS

Satpal Singh; Devendra Kumar; Higinio Ramos

doi:10.11948/20220446

2023 Volume 13 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(4): 2203-2228

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Satpal Singh, Devendra Kumar, Higinio Ramos. AN EFFICIENT PARAMETER UNIFORM SPLINE-BASED TECHNIQUE FOR SINGULARLY PERTURBED WEAKLY COUPLED REACTION-DIFFUSION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2203-2228. doi: 10.11948/20220446

Citation:

Satpal Singh, Devendra Kumar, Higinio Ramos. AN EFFICIENT PARAMETER UNIFORM SPLINE-BASED TECHNIQUE FOR SINGULARLY PERTURBED WEAKLY COUPLED REACTION-DIFFUSION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2203-2228. doi: 10.11948/20220446

AN EFFICIENT PARAMETER UNIFORM SPLINE-BASED TECHNIQUE FOR SINGULARLY PERTURBED WEAKLY COUPLED REACTION-DIFFUSION SYSTEMS

1.
Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan-333031, India
2.
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
3.
Escuela Politécnica Superior de Zamora, Campus Viriato, 49029 Zamora, Spain

Author Bio: Email: dkumar@pilani.bits-pilani.ac.in(D. Kumar); Email: higra@usal.es(H. Ramos)
Corresponding author: Email: satpalsingh1704@gmail.com(S. Singh)

Abstract

Abstract

A parameter-uniform numerical scheme for a system of weakly coupled singularly perturbed reaction-diffusion equations of arbitrary size with appropriate boundary conditions is investigated. More precisely, quadratic $B$-spline basis functions with an exponentially graded mesh are used to solve a $\ell\times\ell$ system whose solution exhibits parabolic (or exponential) boundary layers at both endpoints of the domain. A suitable mesh-generating function is used to generate the exponentially graded mesh. The decomposition of the solution into regular and singular components is obtained to provide error estimates. A convergence analysis is addressed, which shows a uniform convergence of the second order. To validate the theoretical findings, two test problems are solved numerically.
- Singularly perturbed system /
- reaction-diffusion equations /
- param-eter-uniform convergence /
- exponentially graded mesh /
- boundary layers
MSC: 65L10, 65L11, 65L60, 65M50

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References

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