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