An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis

• Published in: Mathematical modelling and analysis Vol. 28; no. 1; pp. 163 - 179
• Main Author: Rostami, Yaser
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.01.2023
• Subjects: Accuracy; Analysis; Applications of mathematics; Applied mathematics; Approximation; Boundary conditions; Boundary value problems; Convergence; Differential equations; Error analysis; Exact solutions; Galerkin method; Hermite wavelet; Integral equations; Methods; Partial differential equations; Polynomials; Volterra integral equations; Volterra partial integro-differential equation; Wavelet analysis; Hermite wavelet; Galerkin method; Volterra partial integro-differential equation
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2023.15690

In this research article Hermite wavelet based Galerkin method is developed for the numerical solution of Volterra integro-differential equations in onedimension with initial and boundary conditions. These equations include the partial differential of an unknown function and the integral term containing the unknown function which is the memory of the problem. Wavelet analysis is a recently developed mathematical tool in applied mathematics. For this purpose, Hermit wavelet Galerkin method has proven a very powerful numerical technique for the stable and accurate solution of giving boundary value problem. The theorem of convergence analysis and compare some numerical examples with the use of the proposed method and the exact solutions shows the efficiency and high accuracy of the proposed method. Several figures are plotted to establish the error analysis of the approach presented.