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Cubic spline and invariant imbedding for solving singular two-point boundary value problems. (English) Zbl 0595.65089

A cubic spline approximation combined with an invariant imbedding method is applied to boundary value problems involving a regular singularity at one end of the interval of consideration. The procedure adopted by the paper is now more or less a standard approach for linear ordinary differential equations using a series expansion about the singular point and matched with a smooth solution (in this case spline), away from the singular point. However, the method has an advantage in that the coefficient matrix of the system is tridiagonal and the method has an order of convergence \(O(h^ 4)\), where h is the step size. The paper is very well written with a useful brief account of some numerical treatments of the class of problem considered.
Reviewer: P.Onumanyi

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
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