Numerical Scheme with Convergence Analysis and Error Estimate for Variable Order Weakly Singular Integro-Differential Equation

被引：4

作者：

Yadav, Poonam ^{[1
]}

Singh, B. P. ^{[2
]}

Alikhanov, Anatoly A. ^{[2
]}

Singh, Vineet Kumar ^{[1
]}

机构：

[1] Banaras Hindu Univ, Indian Inst Technol, Dept Math Sci, Varanasi, Uttar Pradesh, India

[2] Galgotias Univ, Dept Math, Greater Noida 201310, Uttar Pradesh, India

来源：

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2023年 / 20卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Variable order weakly singular integro-differential equation; Caputo derivative; Legendre wavelets; interpolating scaling function; operational matrix; convergence analysis; PARTIAL-DIFFERENTIAL-EQUATIONS; OPERATIONAL MATRIX APPROACH; REPRODUCING KERNEL-METHOD; FRACTIONAL DIFFUSION; COLLOCATION METHOD; LEGENDRE WAVELETS; STABILITY; APPROXIMATION; MECHANICS; MODEL;

D O I：

10.1142/S0219876222500463

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper represents a new application of Legendre wavelet and interpolating scaling function to discuss the approximate solution of variable order integro-differential equation having weakly singular kernel. So far, this technique has been used to solve variable order integro differential equation. In this paper, it is extended to solve variable order integro differential equation with weakly singular kernel. For this purpose, we derive the operational matrices of Legendre wavelets and interpolating scaling function. The resulting operational matrices along with the collocation method transform the original problem into a system of algebraic equation. By solving this system, the approximate solution is obtained. The convergence and error estimate of the presented method have been rigorously investigated. We also discuss the numerical stability of the method. The numerical result of some inclusive examples has been provided through a table and graph for both basis functions that support the robustness and desired precision of the method.

引用

页数：39