scholarly journals An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations

2015 ◽  
Vol 85 (299) ◽  
pp. 1309-1333 ◽  
Author(s):  
Sebastian Kestler ◽  
Kristina Steih ◽  
Karsten Urban
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Space Time ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Adaptive Wavelet ◽  
Wavelet Galerkin Method ◽  
Time Periodic

Wavelet Galerkin method for fourth-order multi-dimensional elliptic partial differential equations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850045 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
Gopal Priyadarshi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Computational Cost ◽  
Stability Estimates ◽  
Partial Differential ◽  
Wavelet Galerkin Method

We describe a wavelet Galerkin method for numerical solutions of fourth-order linear and nonlinear partial differential equations (PDEs) in 2D and 3D based on the use of Daubechies compactly supported wavelets. Two-term connection coefficients have been used to compute higher-order derivatives accurately and economically. Localization and orthogonality properties of wavelets make the global matrix sparse. In particular, these properties reduce the computational cost significantly. Linear system of equations obtained from discretized equations have been solved using GMRES iterative solver. Quasi-linearization technique has been effectively used to handle nonlinear terms arising in nonlinear biharmonic equation. To reduce the computational cost of our method, we have proposed an efficient compression algorithm. Error and stability estimates have been derived. Accuracy of the proposed method is demonstrated through various examples.

An Efficient Modified Taylor Wavelet Galerkin Method for One Dimensional Partial Differential Equations

2021 ◽  
Vol 14 ◽  
Author(s):  
Ankit Kumar ◽  
Sag Ram Verma
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Galerkin Method ◽  
Difference Method ◽  
Partial Differential ◽  
One Dimensional ◽  
Wavelet Galerkin Method

Background: In this paper, a modified Taylor wavelet Galerkin method (MTWGM) based on approximation scheme is used to solve partial differential equations (PDEs), which is play an important role in electrical circuit models. Objective: The objective of this work is to give fine and accurate implementation of proposed method for the solution of PDEs, which is the best tool for the analysis of electric circuit problems. Methods: In this work, we used an effective, modified Taylor wavelet Galerkin method with its residual technique and we obtained more accurate numerical solution of the one dimensional PDEs. The Introduced wavelet method is more efficiently applicable in the comparison of some existing numerical methods such as, finite difference method, finite element method, finite volume method, spectral method etc. This method is the best tool for solving PDEs. Therefore, it has significance in the field of electrical engineering and others. Results: The experimentally four numerical problems are given which are showing the numerical results extractive by introduced method and those results compared with exact solution and other available numerical methods i.e., Hermite wavelet Galarkin method (HWGM), Finite difference method (FDM) and spectral procedures which shows that proposed method is more effective. Conclusion: This work is significantly helpful for the electrical circuits in which the governing models are available in the form of PDEs.

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