Using Runge–Kutta method for numerical solution of the system of Volterra integral equation

摘要

In this paper we introduce some of general methods of Runge–Kutta, they are using for numerical solution of Volterra integral equations of the second kind [H. Brunner, P.J. Vander Houwen, The numerical solution of Volterra Equation, CWI monograph 3, North-Holland, Amsterdam, 1986; P.W. Sharp, J.H. Verner, Extended explicit Bel’tyukov pairs of orders 4 and Volterra integral equations of the second kind, Appl. Numer. Math. (from author’s Homepage)]. We first introduce Pouzet Volterra Runge–Kutta methods (implicit and explicit forms) PVRK, and then explain about some extended explicit Bel’tyukov pairs, EBVRK.Each pair uses six stages and consists of on order 3 formula completely embedded in order 4 formula. In numerical examples this method uses for solving a system of Volterra integral equations and comparison with iterative methods (as [Comput. Math. Appl. 37 (1999) 1; Nonlinear Stud. 6 (1) (1999)]).