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On a fourth-order finite-difference method for singularly perturbed boundary value problems. (English) Zbl 1160.65037
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.

MSC:
65L10Boundary value problems for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE
65L12Finite difference methods for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)
65L50Mesh generation and refinement (ODE)
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References:
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