A quadrature method with variable step for solving linear Volterra integral equations of the second kind

Abstract

In usual quadrature methods for solving integral equations, divide the integration interval ( a, b) into n equal subintervals of the length h = ( b − a)/ n. In this article, we intend to divide the integration interval into n subintervals of different lengths, which solves linear Volterra integral equations more accurately than usual quadrature methods. For further information on quadrature methods with variable step see [L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, 1985; L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, 1974].