论文标题
一种用于非线性弱奇异分数差异方程式的光谱方法
A spectral approach to non-linear weakly singular fractional integro-differential equations
论文作者
论文摘要
在这项工作中，考虑了一类非线性弱奇异的分数差异方程式，我们首先证明解决方案在某些假设上对给定数据的某些假设的存在，唯一性和平滑度。我们提出了一种基于光谱彼得 - 加利尔金方法的数值方法，该方法处理解决方案的非平滑行为。我们方法的最杰出特征是，尽管解决了复杂的非线性代数系统，但通过复发关系来评估近似解决方案。此外，众所周知的指数准确性是在$ l^{2} $ - 规范中建立的，我们提供了一些示例来说明理论结果和所提出方法的性能。
In this work, a class of non-linear weakly singular fractional integro-differential equations is considered, and we first prove existence, uniqueness, and smoothness properties of the solution under certain assumptions on the given data. We propose a numerical method based on spectral Petrov-Galerkin method that handling to the non-smooth behavior of the solution. The most outstanding feature of our approach is to evaluate the approximate solution by means of recurrence relations despite solving complex non-linear algebraic system. Furthermore, the well-known exponential accuracy is established in $L^{2}$-norm, and we provide some examples to illustrate the theoretical results and the performance of the proposed method.
