Sixth-Order Compact Extended Trapezoidal Rules for 2D Schrödinger Equation (Journal of Mathematical Study, 2018)
Based on high-order linear multistep methods (LMMs), we use the classof extended trapezoidal rules (ETRs) to solve boundary value problems of ordinarydifferential equations (ODEs), whose numerical solutions can be approximated byboundary value methods (BVMs). Then we combine this technique with fourth-orderPadé compact approximation to discrete 2D Schrödinger equation. We propose ascheme with sixth-order accuracy in time and fourth-order accuracy in space. It isunconditionally stable due to the favourable property of BVMs and ETRs. Furthermore,with Richardson extrapolation, we can increase the scheme to order 6 accuracyboth in time and space. Numerical results are presented to illustrate the accuracy ofour scheme.