Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions

2006 ◽  
Vol 67 (13) ◽  
pp. 1811-1829 ◽  
Author(s):  
S. Y. Reutskiy ◽  
C. S. Chen
Keyword(s):  
Chebyshev Polynomial ◽  
Basis Functions ◽  
Multivariate Functions ◽  
Particular Solutions ◽  
Trigonometric Basis Functions

scholarly journals THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS

2011 ◽  
Vol 08 (03) ◽  
pp. 545-559 ◽  
Author(s):  
C. S. CHEN ◽  
C. M. FAN ◽  
P. H. WEN
Keyword(s):  
Solution Process ◽  
Fundamental Solutions ◽  
Variable Coefficients ◽  
Basis Functions ◽  
Method Of Fundamental Solutions ◽  
Left Hand ◽  
Particular Solutions ◽  
Particular Solution ◽  
The Right ◽  
Close Form

A new version of the method of approximate particular solutions (MAPSs) using radial basis functions (RBFs) has been proposed for solving a general class of elliptic partial differential equations. In the solution process, the Laplacian is kept on the left-hand side as a main differential operator. The other terms are moved to the right-hand side and treated as part of the forcing term. In this way, the close-form particular solution is easy to obtain using various RBFs. The numerical scheme of the new MAPSs is simple to implement and yet very accurate. Three numerical examples are given and the results are compared to Kansa's method and the method of fundamental solutions.

Timoshenko beam finite elements using trigonometric basis functions

AIAA Journal ◽  
1988 ◽  
Vol 26 (11) ◽  
pp. 1378-1386 ◽  
Author(s):  
G. R. Heppler ◽  
J. S. Hansen
Keyword(s):  
Finite Elements ◽  
Timoshenko Beam ◽  
Basis Functions ◽  
Trigonometric Basis Functions
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