A robust numerical technique for weakly coupled system of parabolic singularly perturbed reaction–diffusion equations
- Resource Type
- Original Paper
- Authors
- Singh, Satpal; Kumar, Devendra; Vigo-Aguiar, J.
- Source
- Journal of Mathematical Chemistry. 61(6):1313-1350
- Subject
- Singularly perturbed problem
Weakly coupled system of PDEs
Boundary layer
Parameter-uniform convergence
Exponentially graded mesh
35B25
35B50
35K51
35K57
65L70
65M12
65M15
65M22
65M50
- Language
- English
- ISSN
- 0259-9791
1572-8897
This article presents a uniformly convergent numerical technique for a time-dependent reaction-dominated singularly perturbed system, including the same diffusion parameters multiplied with second-order spatial derivatives in all equations. Boundary layers are observed in the solution components for the small parameter. The proposed numerical technique consists of the Crank–Nicolson scheme in the temporal direction over a uniform mesh and quadratic B-splines collocation technique over an exponentially graded mesh in the spatial direction. We derived the robust error estimates to establish the optimal order of convergence. Numerical investigations confirm the theoretical determinations and the proposed method’s efficiency and accuracy.