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A mixed decomposition-spline approach for the numerical solution of a class of singular boundary value problems. (English) Zbl 1459.65115
Summary: In this paper, we formulate a patching scheme to solve numerically a class of boundary value problems. The strategy is being founded on a merger of two methods, a modified decomposition technique applied on a small interval near the singularity and a fourth order spline collocation technique which is used on the rest of the domain of the problem. The convergence of the proposed method is analyzed and a fourth-order rate of convergence is proved. Some examples are given to test the efficiency of the scheme and to verify the order of the rate of convergence. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods.
MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
Software:
COLSYS
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References:
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