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Numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation. (English) Zbl 1072.65168
Numerical solutions of linear Volterra integral equations of the first and second kind and Fredholm integral equations of the second kind are obtained by means of the sinc collocation method based on the double exponential transformation. A formula for numerical indefinite integration, developed earlier by M. Muhammad and M. Mori [ibid. 161, No. 2, 431–448 (2003; Zbl 1038.65018)], is applied to the Volterra integral equations. On the other hand, the conventional double exponential transformation for definite integrals is employed to the Fredholm integral equations.
An error analysis of the method is given and in each case a convergence rate of $$O(\exp(-cN/\log N))$$ for the error is established, where $$N$$ is a parameter representing the number of terms of the sinc expansion. Numerical examples are given to show the above mentioned convergence rate and to confirm the high efficiency of the present method.

##### MSC:
 65R20 Numerical methods for integral equations 45D05 Volterra integral equations 45B05 Fredholm integral equations
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