Numerical solution of linear integral equations by using Sinc–collocation method

2005 ◽  
Vol 168 (2) ◽  
pp. 806-822 ◽  
Author(s):  
J. Rashidinia ◽  
M. Zarebnia
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Linear Integral ◽  
Linear Integral Equations

scholarly journals Numerical solution of linear integral equations system using the Bernstein collocation method

2013 ◽  
Vol 2013 (1) ◽  
pp. 123 ◽  
Author(s):  
Ahmad Jafarian ◽  
Safa A Measoomy Nia ◽  
Alireza K Golmankhaneh ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Linear Integral ◽  
Linear Integral Equations

A note on the numerical solution of certain non-linear integral equations

1956 ◽  
Vol 236 (1207) ◽  
pp. 529-534 ◽  
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Asymptotic Form ◽  
Essential Singularity ◽  
Non Linear ◽  
Linear Integral ◽  
Hydrodynamical Problem ◽  
Linear Integral Equations

Methods are described for the numerical solution of two non-linear integral equations occurring in a hydrodynamical problem. In each case the existence of an essential singularity of the solution requires the application of special techniques. The asymptotic form of the solutions for large x is determined.

The numerical solution of non-singular linear integral equations

1953 ◽  
Vol 245 (902) ◽  
pp. 501-534 ◽  
Keyword(s):  
Finite Difference ◽  
Eigenvalue Problem ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Numerical Quadrature ◽  
Iterative Processes ◽  
Upper Limit ◽  
Linear Integral ◽  
Linear Integral Equations

The integral equations discussed and illustrated are those of Fredholm, with fixed limits in the integral and including the eigenvalue problem, and of Volterra, with a variable upper limit in the integral. The methods are mostly based on finite-difference theory, the integrals being replaced by formulae for numerical quadrature. Computational details are given for several methods, and there is a discussion of error analysis for Volterra’s equation. Some methods are given for accelerating the convergence of classical iterative processes.

The numerical solution of integral equations using Chebyshev polynomials

1960 ◽  
Vol 1 (3) ◽  
pp. 344-356 ◽  
Author(s):  
David Elliott
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Chebyshev Polynomials ◽  
Unknown Function ◽  
Chebyshev Series ◽  
Direct Expansion ◽  
Linear Integral ◽  
Polynomial Expansions ◽  
Linear Integral Equations

An investigation has been made into the numerical solution of non-singular linear integral equations by the direct expansion of the unknown function f(x) into a series of Chebyshev polynomials of the first kind. The use of polynomial expansions is not new, and was first described by Crout [1]. He writes f(x) as a Lagrangian-type polynomial over the range in x, and determines the unknown coefficients in this expansion by evaluating the functions and integral arising in the equation at chosen points xi. A similar method (known as collocation) is used here for cases where the kernel is not separable. From the properties of expansion of functions in Chebyshev series (see, for example, [2]), one expects greater accuracy in this case when compared with other polynomial expansions of the same order. This is well borne out in comparison with one of Crout's examples.

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