Parameter-uniform numerical scheme for singularly perturbed parabolic convection–diffusion Robin type problems with a boundary turning point

Gelu, Fasika Wondimu; Duressa, Gemechis File

doi:10.1016/j.rinam.2022.100324

Cited by 10 publications

(1 citation statement)

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“…However, only few studies of one-parameter singularly perturbed parabolic problems of convection-diffusion and reaction-diffusion type subject to Robin boundary conditions are there, for example, see [31]- [40]. Recently, authors in [41] studied two-parameter singularly perturbed parabolic convectiondiffusion-reaction problems with Robin boundary condition where they employed Haar wavelet method for space on a Shishkin mesh and the implicit Euler method for time on a uniform mesh.…”

Section: Introductionmentioning

confidence: 99%

Accelerated Non-standard Numerical Methodfor Two-Parameter Singularly Perturbed Parabolic Problems with Robin Boundary Condition

Gelu

Duressa

2022

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This study devised a robust second-order numerical scheme tosolve two-parameter singularly perturbed parabolic problems with Robin boundary condition. On uniform meshes, the problem is discretized using the implicit Euler method in the time directionand the non-standard finite difference method in the space direction. Also, Robin boundary condition is discretized using the concept of the non-standard finite difference method. The first-order ε-uniform convergence is investigated in both time and space. Applying the Richardson extrapolation technique, the accuracy and convergence rate of the present method have improved from first-orderto second-order. Both theoretical findings and numerical results areagreed upon based on computations of two numerical examples.

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Section: Introductionmentioning

confidence: 99%