Numerical Solution of PDE Using Two Dimensional Chebyshev Wavelet Collocation Method
V.Sumathi1, S. Hemalatha2, B.Sripathy3
1V.Sumathi, Department of Mathematics, Sri Sairam Engineering College, Chennai (TamilNadu), India.
2S. Hemalatha, Department of Mathematic, S.D.N.B Vaishnav College for Women, Chennai (TamilNadu), India.
3B.Sripathy, Department of Mathematics, Sastra University, Thanjavur.
Manuscript received on 01 February 2019 | Revised Manuscript received on 07 February 2019 | Manuscript Published on 13 February 2019 | PP: 268-273 | Volume-8 Issue- 4S February 2019 | Retrieval Number: DS2873028419/2019©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this current work, we investigate a new computational scheme to solve a system of Partial Differential Equations. To handle this method, we initially construct a Two Dimensional Chebyshev wavelet which is used to transform the PDE’s to a linear system of algebraic equations. We approximate the obtained algebraic equations using collocation method. This algorithm can be easily implemented to solve PDE with boundary conditions. We illustrate with examples to analyze the convergence using this Two Dimensional Chebyshev collocation method. Finally, we show the validity, efficiency and applicability of this new technique with some Numerical Examples.
Keywords: Two Dimensional Chebyshev Wavelets, Operational Matrices, Collocation points.
Scope of the Article: Applied Mathematics and Mechanics