Explicit pseudo two-step exponential Runge–Kutta methods for the numerical integration of first-order differential equations

Abstract

This paper is devoted to the explicit pseudo two-step exponential Runge–Kutta (EPTSERK) methods for the numerical integration of first-order ordinary differential equations. These methods inherit the structure of explicit pseudo two-step Runge–Kutta methods and explicit exponential Runge–Kutta methods. We analyze the order conditions and the global errors of the new methods. The new methods are of order s + 1 with s-stages for some suitable nodes. Numerical experiments are reported to show the convergence and the efficiency of the new methods.