Wavelet–Galerkin method for integro–differential equations

2000 ◽  
Vol 32 (3) ◽  
pp. 247-254 ◽  
Author(s):  
A. Avudainayagam ◽  
C. Vani
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Wavelet Galerkin Method

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.

scholarly journals 1st-Order Shear Deformable Beam Formulation Based on Meshless Wavelet Galerkin Method

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
JunHyung Jo ◽  
Yun Lee
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Stiffness Matrix ◽  
Condition Numbers ◽  
Exact Integration ◽  
First Order ◽  
Reduced Integration ◽  
Wavelet Galerkin Method ◽  
Shear Deformable Beam ◽  
Shear Deformable

This paper examined and discussed a Meshless Wavelet Galerkin Method (MWGM) formulation for a first-order shear deformable beam, the properties of the MWGM, the differences between the MWGM and EFG, and programming methods for the MWGM. The first-order shear deformable beam (FSDB) consists of a pair of second-order elliptic differential equations. The weak forms of two differential equations are deduced using Hat wavelet series. The exact integration and reduced integration were used to analyze the problems. Some indeterminate beam problems are considered. Condition numbers of the stiffness matrix were analyzed with exact integration and reduced integration for two cases of these problems. Consequently, the results were converged on the analytic solutions. The shear-locking phenomenon also occurred in the MWGM as it occurs in the conventional FEM. The stiffness matrix calculated from the reduced integration causes a similar numerical error to the stiffness matrix calculated from the exact integration in the MWGM. The MWGM showed desirable results in the examples.

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