A Method for the Numerical Solution of Two-Point Boundary Value Problems Based on the Use of Volterra Integral.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Suppose that a given two-point boundary value problem to be solved is a perturbation of one for which a considerable amount of analytic information is available, in particular, the Greens function of the unperturbed problem is known. In this case, one can construct an analytic method for the solution of the perturbed problem which involves only the solution of a Volterra integral equation. Discretization of this method, which is a version of the classical shooting procedure, leads to a numerical technique for the solution of perturbed boundary value problems. Under suitable assumptions, convergence of the numerical method is established, and estimates are obtained for the rate of convergence. Attention is devoted to the cases in which the unperturbed differential operator is regular or mildly singular. Linear and nonlinear problems are considered. Modified author abstract
- Theoretical Mathematics