Comparative Study of Finite Element and Haar Wavelet Correlation Method for the Numerical Solution of Parabolic Type Partial Differential Equations
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@Article{JICS-11-188,
author = {S. C. Shiralashetti , P. B. Mutalik Desai and A. B. Deshi},
title = {Comparative Study of Finite Element and Haar Wavelet Correlation Method for the Numerical Solution of Parabolic Type Partial Differential Equations},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {11},
number = {3},
pages = {188--207},
abstract = {In this paper, we present the comparative study of Haar wavelet collocation method (HWCM) and
Finite Element Method (FEM) for the numerical solution of parabolic type partial differential equations such
as 1-D singularly perturbed convection-dominated diffusion equation and 2-D Transient heat conduction
problems validated against exact solution. The distinguishing feature of HWCM is that it provides a fast
converging series of easily computable components. Compared with FEM, this approach needs substantially
shorter computational time, at the same time meeting accuracy requirements. It is found that higher accuracy
can be attained by increasing the level of Haar wavelets. As Consequences, it avoids more computational costs,
minimizes errors and speeds up the convergence, which has been justified in this paper through the error
analysis.
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22512.html}
}
TY - JOUR
T1 - Comparative Study of Finite Element and Haar Wavelet Correlation Method for the Numerical Solution of Parabolic Type Partial Differential Equations
AU - S. C. Shiralashetti , P. B. Mutalik Desai and A. B. Deshi
JO - Journal of Information and Computing Science
VL - 3
SP - 188
EP - 207
PY - 2024
DA - 2024/01
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22512.html
KW - Haar wavelet collocation method, parabolic equation, Finite difference method, Finite element
method, Heat conduction problems.
AB - In this paper, we present the comparative study of Haar wavelet collocation method (HWCM) and
Finite Element Method (FEM) for the numerical solution of parabolic type partial differential equations such
as 1-D singularly perturbed convection-dominated diffusion equation and 2-D Transient heat conduction
problems validated against exact solution. The distinguishing feature of HWCM is that it provides a fast
converging series of easily computable components. Compared with FEM, this approach needs substantially
shorter computational time, at the same time meeting accuracy requirements. It is found that higher accuracy
can be attained by increasing the level of Haar wavelets. As Consequences, it avoids more computational costs,
minimizes errors and speeds up the convergence, which has been justified in this paper through the error
analysis.
S. C. Shiralashetti , P. B. Mutalik Desai and A. B. Deshi. (2024). Comparative Study of Finite Element and Haar Wavelet Correlation Method for the Numerical Solution of Parabolic Type Partial Differential Equations.
Journal of Information and Computing Science. 11 (3).
188-207.
doi:
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