A linearized compact finite difference scheme for Schrödinger- Poisson System
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@Article{JICS-13-311,
author = {ChenyiZhu and Huawei Zhao},
title = {A linearized compact finite difference scheme for Schrödinger- Poisson System},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {13},
number = {4},
pages = {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.
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22440.html}
}
TY - JOUR
T1 - A linearized compact finite difference scheme for Schrödinger- Poisson System
AU - ChenyiZhu and Huawei Zhao
JO - Journal of Information and Computing Science
VL - 4
SP - 311
EP - 320
PY - 2024
DA - 2024/01
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22440.html
KW - Schrödinger-Poisson system, local extrapolation technique, compact finite difference
scheme, conservation laws, optimal error estimates.
AB - 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.
ChenyiZhu and Huawei Zhao. (2024). A linearized compact finite difference scheme for Schrödinger- Poisson System.
Journal of Information and Computing Science. 13 (4).
311-320.
doi:
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