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On the numerical solution of linear and nonlinear Volterra integral and integro-differential equations. (English) Zbl 1204.65158

Summary: Sinc bases are developed to approximate the solutions of linear and nonlinear Volterra integral and integro-differential equations. Properties of these sinc bases and some operational matrices are first presented. These properties are then used to reduce the integral and integro-differential equations to systems of linear or nonlinear algebraic equations. Numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems. The examples include convolution type, singular as well as singularly-perturbed problems.

MSC:

65R20 Numerical methods for integral equations
45G05 Singular nonlinear integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
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