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Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions. (English) Zbl 1135.65043
Summary: We use operational matrices of piecewise constant orthogonal functions on the interval \([0,1)\) to solve Volterra integral and integro-differential equations of convolution type without solving any system. We first obtain the Laplace transform of the problem and then we find the numerical inversion of the Laplace transform by operational matrices. Numerical examples show that the approximate solutions have a good degree of accuracy.

MSC:
65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45J05 Integro-ordinary differential equations
44A10 Laplace transform
65R10 Numerical methods for integral transforms
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