Fourth order partial differential equations for Krall-type orthogonal polynomials on the triangle

2018 ◽  
Vol 146 (9) ◽  
pp. 3961-3974
Author(s):  
Antonia M. Delgado ◽  
Lidia Fernández ◽  
Teresa E. Pérez
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Fourth Order ◽  
Partial Differential

scholarly journals Fourth order partial differential equations on general geometries

2006 ◽  
Vol 216 (1) ◽  
pp. 216-246 ◽  
Author(s):  
John B. Greer ◽  
Andrea L. Bertozzi ◽  
Guillermo Sapiro
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Partial Differential

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.

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