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Weak formulation based Haar wavelet method for solving differential equations

机译：基于弱公式的Haar小波方法求解微分方程

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摘要

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.
机译：提出了一种基于Haar小波的离散化求解微分方程的方法。非线性Burgers方程被视为一个测试问题。讨论了基于强公式和弱公式的方法。提出的离散化方案基于弱公式。试图结合FEM和Haar小波的优点。获得的数值结果已针对封闭形式的解析解以及FEM结果进行了验证。已经观察到与确切解决方案的良好一致性。

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