Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel
Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel
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DOI：
10.1155/2021/9968237
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发表时间：
2021-07
影响因子：
1.4
通讯作者：
Guodong Shi;Yanlei Gong;M. Yi
中科院分区：
文献类型：
--
作者：
Guodong Shi;Yanlei Gong;M. Yi
本文给出了求解一类弱奇异非线性分数阶积分微分方程数值解的数值格式。这种方法利用了交替的勒让德多项式。一个基于交替勒让德多项式的运算矩阵被导出来近似这类方程的奇异核。利用积分和积的运算矩阵及其导出的运算矩阵，将非线性分数阶积分微分方程转化为非线性代数方程组。此外，还分析了该方法的收敛性，特别是误差分析。此外，重要的数值应用结果也以图表和表格的形式记录下来，以详细说明所提出方法的有效性和准确性。
In this paper, we present a numerical scheme for finding numerical solution of a class of weakly singular nonlinear fractional integro-differential equations. This method exploits the alternative Legendre polynomials. An operational matrix, based on the alternative Legendre polynomials, is derived to be approximated the singular kernels of this class of the equations. The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. Moreover, results of essential numerical applications have also been documented in a graphical as well as tabular form to elaborate the effectiveness and accuracy of the proposed method.