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Nonpolynomial spline finite difference scheme for nonlinear singuiar boundary value problems with singular perturbation and its mechanization

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  • A general scheme for the numerical solution of nonlinear singular perturbation problems using nonpolynomial spline basis is proposed in the paper. The special non-equidistant formulation of mesh takes into account the boundary and interior layer structures. The proposed scheme is almost fourth order accurate and applicable to both singular and nonsingular cases. Convergence analysis of the scheme is briefly discussed. Maple program for the generation of difference scheme is presented. Computational illustrations characterized by boundary and interior layers show that the practical order of accuracy is close to the theoretical order of the method.
    Mathematics Subject Classification: Primary: 65L10, 65L12; Secondary: 34B16.

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