Using crooked lines for the higher accuracy in system of integral equations

The numerical solution to the linear and nonlinear and linearsystem of Fredholm and Volterra integral equations of the second kind areinvestigated. We have used crooked lines which includ the nodes speci¯edby modi¯ed rationalized Haar functions. This method di®ers from usingnominal Haar or Walsh wavelets. The accuracy of the solution is improvedand the simplicity of the method of using nominal Haar functions is pre-served. In this paper, the crooked lines with unknown coe±cients underthe speci¯ed conditions change the system of integral equations to a systemof equations. By solving this system the unknowns are obtained and thecrooked lines are determined. Finally, error analysis of the procedure areconsidered and this procedure is applied to the numerical examples, whichillustrate the accuracy and simplicity of this method in comparison withthe methods proposed by these authors.