A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model

A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model

Year:    2014

Author:    Hai-Yan Cao, Zhi-Zhong Sun, Xuan Zhao

Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-m1295

Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 3 : pp. 281–298

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Magneto-thermo-elasticity conservation finite difference solvability stability convergence.

Author Details

Hai-Yan Cao

Zhi-Zhong Sun

Xuan Zhao