High-order compact schemes for semilinear parabolic moving boundary problems

摘要

In this paper, we study high-order compact schemes for semilinear parabolic moving boundary problems. We first convert the original problem into an equivalent one defined on a rectangular region by introducing a linear transformation and the well-known exponential transformation. Next, we derive a compact scheme with fourth-order accuracy in the spatial dimension and second-order accuracy in the temporal dimension. Moreover, we prove that the numerical solutions are convergent strictly in the maximum norm by an energy argument. Extending to two-dimensional semilinear moving boundary problems is also provided. Finally, a series of numerical experiments including linear and semilinear examples are carried out to verify that our schemes have more advantages than the one proposed only for the linear moving boundary problem by Cao and Sun (2010) [6].