A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations

in this paper, we propose an efficient numerical method for solving systems of linear and nonlinear integral equations of the first and second kinds, which avoids the need for special starting values. the method has also the advantages of simplicity of application and at least six order of convergence. a convergence analysis is given and accuracy of the method is clarified by numerical examples. mathematical subject classification: 65r20.