Explicit Runge-Kutta methods for the numerical solution of linear inhomogeneous IVPs

Runge-Kutta methods for the numerical solution of inhomogeneous linear initial value problems with constant coefficients are considered.A general procedure to construct explicit s-stage RK methods with order s, for the class of IVP under consideration, depending on the nodes ci, i = 1, ... , s is presented. This procedure only requires the solution of successive linear equations in the elements of the matrix A and avoids the solution of non linear equations.We obtain several RK schemes with number of stages s = 5, ... , 8 and maximal order p = s for the class of problems under consideration. Finally, some numerical experiments to test the behaviour of the new RK schemes are presented.(c) 2023 Elsevier B.V. All rights reserved.