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Pathan, Mahabub Basha; Vembu, Shanthi

A parameter-uniform second order numerical method for a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous convection coefficients and source terms. (English) Zbl 1380.65132

Calcolo 54, No. 3, 1027-1053 (2017).
The authors propose a uniformly convergent numerical scheme for singularly perturbed systems of weakly coupled convection-diffusion two-point boundary value problems (BVPs) with discontinuous convection coefficients and source terms. The solution of this system of BVPs exhibit interior layers. To discretize the domain piecewise-uniform Shishkin meshes are used. The differential equations are approximated by the cubic spline scheme in the interior layer regions, where the meshes are fine, and by the classical finite difference scheme in the outer regions, where the meshes are coarse. At the discontinuity point a one-sided second-order difference scheme is used. The proposed hybrid scheme is almost second-order convergent with a logarithmic term. Theoretical error estimates are obtained, and numerical experiments are carried out.
Reviewer: Srinivasan Natesan (Assam)

Cited in 5 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

singular perturbation; convection-diffusion problems; interior layers; Shishkin meshes; finite difference scheme; cubic spline; error estimates; convergence; numerical experiments
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References:

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