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

This article deals with the numerical solution to the magneto-thermoelasticity 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-infinity-norm of the difference scheme are proved. One numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.