Composite Euler Method for Stochastic Differential Equations with Poisson Jumps

This paper proposes a new numerical method for stochastic differential equations with Poisson jumps (SDEJs), which is called the composite Euler method. This method draws on the strengths and avoids the weaknesses, effectively combining the advantages of the implicit Euler method and the explicit Euler method, and is superior to the single Euler method in terms of stability and convergence. At the end of the paper, numerical verification is carried out on the convergence and stability of the composite Euler method. MR(2020) Subject Classification 65H10; 65C30; 65L20