Galerkin and Collocation Methods

2018 ◽  
pp. 17-31
Author(s):  
George Rawitscher ◽  
Victo dos Santos Filho ◽  
Thiago Carvalho Peixoto
Keyword(s):  
Collocation Methods ◽  
Galerkin And Collocation Methods

On Projective Methods of Approximate Solution of Singular Integral Equations

1996 ◽  
Vol 3 (5) ◽  
pp. 457-474
Author(s):  
A. Jishkariani ◽  
G. Khvedelidze
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Collocation Methods ◽  
Projective Methods ◽  
Galerkin And Collocation Methods

Abstract The estimate for the rate of convergence of approximate projective methods with one iteration is established for one class of singular integral equations. The Bubnov–Galerkin and collocation methods are investigated.

scholarly journals Numerical Approximation of Fredholm Integral Equation (FIE) of 2nd Kind using Galerkin and Collocation Methods

2019 ◽  
Vol 38 ◽  
pp. 11-25
Author(s):  
Hasib Uddin Molla ◽  
Goutam Saha
Keyword(s):  
Exact Solution ◽  
Galerkin Method ◽  
Collocation Method ◽  
Exact Analytical Solution ◽  
Polynomial Solution ◽  
Hermite Polynomials ◽  
Research Work ◽  
Basis Functions ◽  
Collocation Methods ◽  
Galerkin And Collocation Methods

In this research work, Galerkin and collocation methods have been introduced for approximating the solution of FIE of 2nd kind using LH (product of Laguerre and Hermite) polynomials which are considered as basis functions. Also, a comparison has been done between the solutions of Galerkin and collocation method with the exact solution. Both of these methods show the outcome in terms of the approximate polynomial which is a linear combination of basis functions. Results reveal that performance of collocation method is better than Galerkin method. Moreover, five different polynomials such as Legendre, Laguerre, Hermite, Chebyshev 1st kind and Bernstein are also considered as a basis functions. And it is found that all these approximate solutions converge to same polynomial solution and then a comparison has been made with the exact solution. In addition, five different set of collocation points are also being considered and then the approximate results are compared with the exact analytical solution. It is observed that collocation method performed well compared to Galerkin method. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 11-25

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