A Numerical Algorithm for the Schrödinger Type Differential Equation with Time Involution - Ashyralyev, Allaberen; Hidayat, Twana (Sulaimani Journal for Pure and Applied Sciences, 2020)
The initial boundary value problem for the one dimensional (SE) with time involution and Neumann condition is investigated. The theorem on stability this problem is proved. New absolute stable difference schemes (DSs) for this involution problem are constucted. The theorem on stability the first order of accuracy difference scheme is established. The algorithm has been built for these (DSs), a program is written, examples are presented, and numerical results have been tabulated. Comparisons of errors are made between the exact and numerical solutions in maximum norm. All the computer programs are written in Matlab.
Keywords: Schrödinger equation; Involution; Stability; Difference scheme