Canonical Euler splitting method for nonlinear composite stiff evolution equations

In this paper, a new splitting method, called canonical Euler splitting method (CES), is constructed and studied, which can be used for the efficient numerical solution of general nonlinear composite stiff problems in evolution equations of various type, such as ordinary differential equations (ODEs), semi-discrete unsteady partial differential equations (PDEs) and ordinary or partial Volterra functional differential equations (VFDEs), and can significantly improve the computing speed on the basis of ensuring the computing quality. Stability, consistency and convergence theories of this method are established. A series of numerical experiments are given which check the efficiency of CES method and confirm our theoretical results.