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 nonlin-ear composite stiff problems in evolution equations of various type, such as ordinary differential equations (ODEs), unsteady partial differential equations (PDEs) and ordinary or partial Volterra functional differential equations (VFDEs). Stability, consistency and convergence theories of this method are established. A series of numerical experiments are given which check the efficiency of CES and confirm our theoretical results.