A collocation method for solving nonlinear second kind Volterra integral equations through single-term Walsh series

In this paper, a numerical method for solving second kind nonlinear Volterra integral equations is presented. The method is based upon the extension of unknown function by single term Walsh series. Indeed, the interval [0, 1) is divided to m equal subinterval and in each interval, the unknown function is extended by the first term of Walsh series functions. By using a collocation method the coefficients of these extensions are computed and a block-pulse approximation of the unknown function is obtained. By the block-pulse approximation both continuous and pointwise approximations can be obtained. A convergence analysis for continuous approximations are investigated. The numerical examples confirm the ability and accuracy of the method. The method is computationally attractive and can easily be generalized for the systems of nonlinear volterra equations.