A linearized compact finite difference scheme for Schrödinger- Poisson System
Year: 2018
Journal of Information and Computing Science, Vol. 13 (2018), Iss. 4 : pp. 311–320
Abstract
In this paper, a novel high accurate and efficient finite difference scheme is proposed for solving the Schrödinger-Poisson System. Applying a local extrapolation technique in time to the nonlinear part makes the proposed scheme linearized in the implementation. In fact, at each time step, only two tri-diagonal linear systems of algebraic equations are solved by using Thomas method. Another feature of the proposed method is the high spatial accuracy on account of adopting the compact finite difference approximation to discrete the system in space. Moreover, the proposed scheme preserves the total mass in discrete sense. Under certain regularity assumptions of the exact solution, the local truncation error of the proposed scheme is analyzed in detail by using Taylor’s expansion, and consequently the optimal error estimates of the numerical solutions are established by using the standard energy method and a mathematical induction argument. The convergence order is of O(τ 2 + h4) in the discrete L2-norm and L∞-norm, respectively. Numerical results are reported to measure the theoretical analysis, which shows that the new scheme is accurate and efficient and it preserves well the total mass and energy.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2024-JICS-22440
Journal of Information and Computing Science, Vol. 13 (2018), Iss. 4 : pp. 311–320
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10