The mixed Runge–Kutta methods for a class of nonlinear functional-integro-differential equations

In this paper, for a class of nonlinear functional-integro-differential equations, a type of mixed Runge–Kutta methods are presented by combining the underlying Runge–Kutta methods and the compound quadrature rules. Based on the non-classical Lipschitz condition, a global stability criterion is derived. Numerical experiments illustrate applicability of the theory, efficiency of the methods, and difference of the mixed Runge–Kutta methods from the Pouzet–Runge–Kutta methods.