The splitting Crank-Nicolson scheme with intrinsic parallelism for solving parabolic equations (Q2173559)

This article discusses a splitting Crank-Nicolson scheme with intrinsic parallelism for approximating solutions to parabolic equations. The approach relies on using two domain decomposition method which split the Crank-Nicolson scheme; each one is used to solve the values at the same time level. Further, the average of two values is calculated. The splitting Crank-Nicholson preserves the unconditional stability and second-order numerical accuracy. The authors further extend the method to 2D parabolic equations by the alternating direction implicit technique. Some numerical experiments are also included to illustrate the good performance of the proposed approach.