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

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 contai...

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Published inMathematical modelling and analysis Vol. 28; no. 1; pp. 163 - 179
Main Author Rostami, Yaser
Format Journal Article
LanguageEnglish
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
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Abstract 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.
AbstractList 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.
In this research article Hermite wavelet based Galerkin method is developed for the numerical solution of Volterra integro-differential equations in one-dimension 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. Keywords: Volterra partial integro-differential equation, Hermite wavelet, Galerkin method. AMS Subject Classification: 65R20; 45K99.
Audience Academic
Author Rostami, Yaser
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SubjectTerms 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
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Title An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis
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