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Volume 16, Issue 3
A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model

Dingwen Deng & Ruyu Zhang

Adv. Appl. Math. Mech., 16 (2024), pp. 608-635.

Published online: 2024-02

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  • Abstract

This study is concerned with numerical solutions of a Magneto-Thermo-Elasticity (MTE) model via a combination of energy-conserving finite difference method (FDM) with Richardson extrapolation methods (REMs). Firstly, by introducing two auxiliary functions and using second-order centered FDM and Crank-Nicolson method to approximate spatial and temporal derivatives, respectively, a two-level energy-conserving FDM is established for a MTE model. The priori estimation, solvability, and convergence are derived rigorously by using the discrete energy method. Secondly, to improve computational efficiency, a class of REMs are also designed by constructing the symbolic expansion of numerical solutions. Finally, numerical results confirm the efficiency of the proposed algorithms and the exactness of the theoretical findings.

  • AMS Subject Headings

65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-608, author = {Deng , Dingwen and Zhang , Ruyu}, title = {A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {3}, pages = {608--635}, abstract = {

This study is concerned with numerical solutions of a Magneto-Thermo-Elasticity (MTE) model via a combination of energy-conserving finite difference method (FDM) with Richardson extrapolation methods (REMs). Firstly, by introducing two auxiliary functions and using second-order centered FDM and Crank-Nicolson method to approximate spatial and temporal derivatives, respectively, a two-level energy-conserving FDM is established for a MTE model. The priori estimation, solvability, and convergence are derived rigorously by using the discrete energy method. Secondly, to improve computational efficiency, a class of REMs are also designed by constructing the symbolic expansion of numerical solutions. Finally, numerical results confirm the efficiency of the proposed algorithms and the exactness of the theoretical findings.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0202}, url = {http://global-sci.org/intro/article_detail/aamm/22931.html} }
TY - JOUR T1 - A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model AU - Deng , Dingwen AU - Zhang , Ruyu JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 608 EP - 635 PY - 2024 DA - 2024/02 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2022-0202 UR - https://global-sci.org/intro/article_detail/aamm/22931.html KW - Finite difference method, Richardson extrapolation methods, energy conservation, priori estimation, solvability, convergence. AB -

This study is concerned with numerical solutions of a Magneto-Thermo-Elasticity (MTE) model via a combination of energy-conserving finite difference method (FDM) with Richardson extrapolation methods (REMs). Firstly, by introducing two auxiliary functions and using second-order centered FDM and Crank-Nicolson method to approximate spatial and temporal derivatives, respectively, a two-level energy-conserving FDM is established for a MTE model. The priori estimation, solvability, and convergence are derived rigorously by using the discrete energy method. Secondly, to improve computational efficiency, a class of REMs are also designed by constructing the symbolic expansion of numerical solutions. Finally, numerical results confirm the efficiency of the proposed algorithms and the exactness of the theoretical findings.

Dingwen Deng & Ruyu Zhang. (2024). A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model. Advances in Applied Mathematics and Mechanics. 16 (3). 608-635. doi:10.4208/aamm.OA-2022-0202
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