High accuracy combination method for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind (Q980664)

Summary: This paper presents a high accuracy combination algorithm for solving systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of a combination algorithm, we can obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover, an a posteriori error estimation for the algorithm is derived. Both the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational cost.