Weak formulation based Haar wavelet method for solving differential equations |
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Authors: | Jüri Majak Meelis Pohlak Toomas Lepikult |
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Institution: | a Department of Mechanics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia b The Estonian Information Technology College, Raja 4C, 12616 Tallinn, Estonia |
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Abstract: | The Haar wavelet based discretization method for solving differential equations is developed. Nonlinear Burgers equation is considered as a test problem. Both, strong and weak formulations based approaches are discussed. The discretization scheme proposed is based on the weak formulation. An attempt is made to combine the advantages of the FEM and Haar wavelets. The obtained numerical results have been validated against a closed form analytical solution as well as FEM results. Good agreement with the exact solution has been observed. |
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Keywords: | Haar wavelet Weak formulation based solution Shock wave |
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