Solving heat equations under convection boundary conditions by a high-performance space-time boundary shape functions method

摘要

To be a numerical method, the time-dependent convection boundary conditions are hard to be fulfilled exactly, which will deteriorate the accuracy of numerical solution. With this in mind, we develop novel algorithms to find the solutions for 1-D and 2-D heat equations, which can exactly satisfy the initial condition and convection boundary conditions. A new idea of space-time boundary shape functions (STBSFs) with two free parameters is introduced, whose existence are proven and they can automatically and exactly satisfy all the specified conditions. We let the STBSFs be the bases of the solution, which not only satisfy all the prescribed conditions automatically, but also can find solution simply by a collocation technique. Numerical examples confirm the high-performance of the STBSF methods (STBSFMs), which provide very accurate solutions and the CPU time is very saving.