An Efficient Modified Taylor Wavelet Galerkin Method for One Dimensional Partial Differential Equations

(E-pub Abstract Ahead of Print)

Author(s): Ankit Kumar, Sag Ram Verma*

Journal Name: Recent Advances in Electrical & Electronic Engineering
Formerly Recent Patents on Electrical & Electronic Engineering

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Background: In this paper, a modified Taylor wavelet Galerkin method (MTWGM) based on approximation scheme is used to solve partial differential equations (PDEs), which is play an important role in electrical circuit models.

Objective: The objective of this work is to give fine and accurate implementation of proposed method for the solution of PDEs, which is the best tool for the analysis of electric circuit problems.

Methods: In this work, we used an effective, modified Taylor wavelet Galerkin method with its residual technique and we obtained more accurate numerical solution of the one dimensional PDEs. The Introduced wavelet method is more efficiently applicable in the comparison of some existing numerical methods such as, finite difference method, finite element method, finite volume method, spectral method etc. This method is the best tool for solving PDEs. Therefore, it has significance in the field of electrical engineering and others.

Results: The experimentally four numerical problems are given which are showing the numerical results extractive by introduced method and those results compared with exact solution and other available numerical methods i.e., Hermite wavelet Galarkin method (HWGM), Finite difference method (FDM) and spectral procedures which shows that proposed method is more effective.

Conclusion: This work is significantly helpful for the electrical circuits in which the governing models are available in the form of PDEs.

Keywords: Wavelet, taylor wavelet, modified taylor wavelet basis, weight function, hermite wavelet galerkin method, finite difference method, partial differential equations.

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Article Details

(E-pub Abstract Ahead of Print)
DOI: 10.2174/2352096514666210217114001
Price: $95