Abstract 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.

中文翻译：

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用高性能时空边界形状函数法求解对流边界条件下的热方程

摘要 作为一种数值方法，瞬态对流边界条件难以准确满足，会降低数值求解的精度。考虑到这一点，我们开发了新颖的算法来寻找一维和二维热方程的解，它们可以完全满足初始条件和对流边界条件。引入了具有两个自由参数的时空边界形状函数（STBSFs）的新思想，证明了其存在性，并且它们可以自动准确地满足所有指定条件。我们让STBSFs作为解的基础，它不仅自动满足所有规定的条件，而且可以简单地通过搭配技术找到解。数值例子证实了 STBSF 方法 (STBSFM) 的高性能，