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