Application of the Haar wavelet transform to solving integral and differential equations
By Ü. Lepik. Proceedings of the Estonian Academy of Sciences : Physics, Mathematics, 2007
180 citations recorded by the source corpus.
A survey on the use of the Haar wavelet method for solving nonlinear integral and differential equations is presented. This approach is applicable to different kinds of integral equations (Fredholm, Volterra, and integro-differential equations). Application to partial differential equations is exemplified by solving the sine-Gordon equation. All these problems are solved with the aid of collocation techniques. Computer simulation is carried out for problems the exact solution of which is known. This allows us to estimate the precision of the obtained numerical results. High accuracy of the results even in the case of a small number of collocation points is observed.
Subfields: Atomic and Molecular Physics, and Optics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/0b647242194e4edd0921bbe18c2d3671183a30fb
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In Atomic and Molecular Physics, and Optics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- Haar wavelet method for solving some nonlinear Parabolic equations (2010, methodology): “Lepik [16–18] had solved higher order as well as nonlinear ODEs and some nonlinear evolution equations by Haar wavelet method.”
- A Comparative Study of a Haar Wavelet Method and a Restrictive Taylor's Series Method for Solving Convection-diffusion Equations (2010, methodology): “Recently, Lepik [17–19] established the Haar wavelet method for solving some ODEs and PDEs.”
- An Overview of Haar Wavelet Method for Solving Differential and Integral Equations (2013, methodology): “A survey of early results in this field can be found in [27].”