A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems

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Abstract

We present a three-point finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problem (xxy′)′ = f(x,y) y(0) = A, y(1) = B, 0≤α<1. We show that the method, based on non-uniform mesh, provides O(h4)-convergent approximations. This method is illustrated by two numerical examples, one is linear and the other is non-linear. © 2001 Elsevier Science B.V. All rights reserved.

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Aziz, T., & Kumar, M. (2001). A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems. Journal of Computational and Applied Mathematics, 136(1–2), 337–342. https://doi.org/10.1016/S0377-0427(00)00624-5

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