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 conta...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2023-01-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://jeelm.vgtu.lt/index.php/MMA/article/view/15690 |
| _version_ | 1797947454903025664 |
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| author | Yaser Rostami |
| author_facet | Yaser Rostami |
| author_sort | Yaser Rostami |
| collection | DOAJ |
| description |
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.
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| first_indexed | 2024-04-10T21:26:56Z |
| format | Article |
| id | doaj.art-4001e9cfc16e4467b31a71227d7504fd |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-04-10T21:26:56Z |
| publishDate | 2023-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-4001e9cfc16e4467b31a71227d7504fd2023-01-19T16:15:03ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102023-01-0128110.3846/mma.2023.15690An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysisYaser Rostami0Department of Mathematic, Malard Branch, Islamic Azad University, Tehran, Iran 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. https://jeelm.vgtu.lt/index.php/MMA/article/view/15690Volterra partial integro-differential equationHermite waveletGalerkin method |
| spellingShingle | Yaser Rostami An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis Mathematical Modelling and Analysis Volterra partial integro-differential equation Hermite wavelet Galerkin method |
| title | An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis |
| title_full | An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis |
| title_fullStr | An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis |
| title_full_unstemmed | An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis |
| title_short | An effective computational approach based on Hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis |
| title_sort | effective computational approach based on hermite wavelet galerkin for solving parabolic volterra partial integro differential equations and its convergence analysis |
| topic | Volterra partial integro-differential equation Hermite wavelet Galerkin method |
| url | https://jeelm.vgtu.lt/index.php/MMA/article/view/15690 |
| work_keys_str_mv | AT yaserrostami aneffectivecomputationalapproachbasedonhermitewaveletgalerkinforsolvingparabolicvolterrapartialintegrodifferentialequationsanditsconvergenceanalysis AT yaserrostami effectivecomputationalapproachbasedonhermitewaveletgalerkinforsolvingparabolicvolterrapartialintegrodifferentialequationsanditsconvergenceanalysis |