arrow
Volume 11, Issue 3
Comparative Study of Finite Element and Haar Wavelet Correlation Method for the Numerical Solution of Parabolic Type Partial Differential Equations

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

J. Info. Comput. Sci. , 11 (2016), pp. 188-207.

Export citation
  • 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.
  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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:
Copy to clipboard
The citation has been copied to your clipboard