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Volume 11, Issue 1
Comparative study of finite element and haar wavelet collocation method for the numerical solution of parabolic type partialdifferential equations

S. C. Shiralashetti , P. B. Mutalik Desai and A. B. Deshi

J. Info. Comput. Sci. , 11 (2016), pp. 016-029.

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  • 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.
  • Keywords

Haar wavelet collocation method, parabolic equation, Finite difference method, Finite element method, Heat conduction problems.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JICS-11-016, author = {S. C. Shiralashetti , P. B. Mutalik Desai and A. B. Deshi}, title = {Comparative study of finite element and haar wavelet collocation method for the numerical solution of parabolic type partialdifferential equations}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {11}, number = {1}, pages = {016--029}, 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/22526.html} }
TY - JOUR T1 - Comparative study of finite element and haar wavelet collocation method for the numerical solution of parabolic type partialdifferential equations AU - S. C. Shiralashetti , P. B. Mutalik Desai and A. B. Deshi JO - Journal of Information and Computing Science VL - 1 SP - 016 EP - 029 PY - 2024 DA - 2024/01 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22526.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 collocation method for the numerical solution of parabolic type partialdifferential equations. Journal of Information and Computing Science. 11 (1). 016-029. doi:
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