On the Construction of Splitting Methods by Stabilizing Corrections with Runge-Kutta Pairs
For researchers in numerical differential equations, this provides a systematic construction of splitting methods, though it is an incremental contribution to existing Runge-Kutta and splitting method theory.
This note presents a general procedure to construct internally consistent splitting methods for differential equations using matching explicit and diagonally implicit Runge-Kutta pairs. The methods are applied to second-order pairs, with linear stability analysis and numerical tests demonstrating their effectiveness.
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta methods. The procedure will be applied to suitable second-order pairs, and we will consider methods with or without a mass conserving finishing stage. For these splitting methods, the linear stability properties are studied and numerical test results are presented.