论文标题
与分数热方程相关的稀疏表示
The sparse representation related with fractional heat equations
论文作者
论文摘要
这项研究介绍了正交前自适应傅里叶分解（POAFD），以获得分数拉普拉斯初始值问题的近似和数值解，以及caffarelli和silvestre的扩展问题（广义泊松方程）。作为第一步，该方法将初始数据功能扩展到具有快速收敛的基本解决方案的稀疏系列中，并且作为第二步，使用了每个扩展条目的semigroup或复制核属性。实验显示了提出的串联解决方案的有效性和效率。
This study introduces pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre (generalized Poisson equation). The method, as the first step, expands the initial data function into a sparse series of the fundamental solutions with fast convergence, and, as the second step, makes use the semigroup or the reproducing kernel property of each of the expanding entries. Experiments show effectiveness and efficiency of the proposed series solutions.
