A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model (Advances in Applied Mathematics and Mechanics, 2014)
This article deals with the numerical solution to themagneto-thermo-elasticity model, which is a system of the third orderpartial differential equations. By introducing a new function, themodel is transformed into a system of the second order generalizedhyperbolic equations. A priori estimate with the conservation forthe problem is established. Then a three-level finite difference scheme isderived. The unique solvability, unconditional stability andsecond-order convergence in $L_{∞}$-norm of the differencescheme are proved. One numericalexample is presented to demonstrate the accuracy and efficiency ofthe proposed method.