Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids
Abstract
The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon equation are used as model equations. Adaptive as well as nonadaptive nonuniform grids are developed and used to solve the model equations numerically. The numerical results are compared to the known analytical solutions as well as to the numerical solutions obtained by application of the HOHWM on a uniform grid. The proposed methods of using nonuniform grid are shown to significantly increase the accuracy of the HOHWM at the same number of grid points.
Keyword : numerical simulation, Haar wavelet method, higher order wavelet expansion, nonlinear PDEs, nonuniform grid, adaptive grid
How to Cite
Ratas, M., Salupere, A., & Majak, J. (2021). Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids. Mathematical Modelling and Analysis, 26(1), 147-169. https://doi.org/10.3846/mma.2021.12920
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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C. Cattani and A. Kudreyko. Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind. Applied Mathematics and Computation, 215(12):4164–4171, 2010. . https://doi.org/10.1016/j.amc.2009.12.037
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