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Zbl 1160.65037
Herceg, Dragoslav; Herceg, Djordje
On a fourth-order finite-difference method for singularly perturbed boundary value problems. (English)
[J] Appl. Math. Comput. 203, No. 2, 828-837 (2008). ISSN 0096-3003

The authors presented a fourth-order finite difference method for singularly perturbed one-dimensional reaction-diffusion boundary-value problems. The domain is discretized by using a layer-adapted Bakhvalov-type mesh. Parameter-uniform convergence results are obtained. Numerical examples are provided to validate the theoretical fourth-order convergence of the method.
[Srinivasan Natesan (Assam)]

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
65L20 Stability of numerical methods for ODE
65L12 Finite difference methods for ODE
34B15 Nonlinear boundary value problems of ODE
34E15 Asymptotic singular perturbations, general theory (ODE)
65L50 Mesh generation and refinement (ODE)

Keywords: singular perturbation; non-equidistant grid; uniform convergence; fourth-order finite difference method; reaction-diffusion boundary-value problems; layer-adapted Bakhvalov-type mesh; numerical examples; fourth-order convergence

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