Volume 6, Issue 3
A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model

Adv. Appl. Math. Mech., 6 (2014), pp. 281-298.

Published online: 2014-06

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• Abstract

This article deals with the numerical solution to the magneto-thermo-elasticity model, which is a system of the third order partial differential equations. By introducing a new function, the model is transformed into a system of the second order generalized hyperbolic equations. A priori estimate with the conservation for the problem is established. Then a three-level finite difference scheme is derived. The unique solvability, unconditional stability and second-order convergence in $L_{\infty}$-norm of the difference scheme are proved. One numerical example is presented  to demonstrate the accuracy and efficiency of the proposed method.

• Keywords

Magneto-thermo-elasticity conservation finite difference solvability stability convergence

65M06 65M12 65M12 78M20 80M20

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@Article{AAMM-6-281, author = {Hai-Yan Cao, Zhi-Zhong Sun and Xuan Zhao}, title = {A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {3}, pages = {281--298}, abstract = {

This article deals with the numerical solution to the magneto-thermo-elasticity model, which is a system of the third order partial differential equations. By introducing a new function, the model is transformed into a system of the second order generalized hyperbolic equations. A priori estimate with the conservation for the problem is established. Then a three-level finite difference scheme is derived. The unique solvability, unconditional stability and second-order convergence in $L_{\infty}$-norm of the difference scheme are proved. One numerical example is presented  to demonstrate the accuracy and efficiency of the proposed method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m1295}, url = {http://global-sci.org/intro/article_detail/aamm/19.html} }
TY - JOUR T1 - A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model AU - Hai-Yan Cao, Zhi-Zhong Sun & Xuan Zhao JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 281 EP - 298 PY - 2014 DA - 2014/06 SN - 6 DO - http://dor.org/10.4208/aamm.12-m1295 UR - https://global-sci.org/intro/article_detail/aamm/19.html KW - Magneto-thermo-elasticity KW - conservation KW - finite difference KW - solvability KW - stability KW - convergence AB -

This article deals with the numerical solution to the magneto-thermo-elasticity model, which is a system of the third order partial differential equations. By introducing a new function, the model is transformed into a system of the second order generalized hyperbolic equations. A priori estimate with the conservation for the problem is established. Then a three-level finite difference scheme is derived. The unique solvability, unconditional stability and second-order convergence in $L_{\infty}$-norm of the difference scheme are proved. One numerical example is presented  to demonstrate the accuracy and efficiency of the proposed method.

Hai-Yan Cao, Zhi-Zhong Sun & Xuan Zhao. (1970). A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model. Advances in Applied Mathematics and Mechanics. 6 (3). 281-298. doi:10.4208/aamm.12-m1295
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