A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations
An efficient block by block numerical methods is proposed in order to solve systems of linear and nonlinear first and second kind Volterra integral equations of Urysohn type. The method is based on the Romberg quadrature rule which involves the trapezoidal or the Simpson quadrature formula and eventually can use the Lagrange interpolation. Due to its simplicity, the method can be easily implemented for an increasing number of blocks and for obtaining better accuracy. The convergence of the method is proved and the order of convergence is at least six. The performances of the method are illustrated on four numerical examples in comparison with the homotopy perturbation method and a modification of the radial basis function network method. Three examples are devoted to second kind integral equations and in another example to integral equations of the first kind. The block by block method is shown to be more effective. The numerical results are obtained by programming in Maple 11.
Urysohn type Volterra integral equations
scientific article; zbMATH DE number 6064104