Unconditionally stable high-order time integration for moving mesh finite difference solution of linear convection-diffusion equations

This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability of numerical schemes. Moreover, many implicit second and higher order schemes, such as the Crank-Nicolson scheme, will loss their unconditional stability. A strategy is presented for developing temporally high order, unconditionally stable finite difference schemes for solving linear convection-diffusion equations using moving meshes. Numerical results are given to demonstrate the theoretical findings.