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∞-norm of the difference scheme are proved.One numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.
The phase field crystal(PFC) model is a nonlinear evolutionary equation that is of sixth order in space.In the first part of this work,we derive a three level linearized difference scheme,which is then proved to be energy stable,uniquely solvable and second order convergent in L_2 norm by the energy method combining with the inductive method.In the second part of the work,we analyze the unique solvability and convergence of a two level nonlinear difference scheme,which was developed by Zhang et al.in 2013.Some numerical results with comparisons are provided.
