scholarly journals On some two dimensional Volterra type linear integral equations with super-singularity

2003 ◽  
Vol 4 (1) ◽  
pp. 65 ◽  
Author(s):  
Nusrat Rajabov ◽  
Miklós Rontó ◽  
Lutfia Rajabova
Keyword(s):  
Integral Equations ◽  
Two Dimensional ◽  
Volterra Type ◽  
Linear Integral ◽  
Linear Integral Equations

scholarly journals Numerical Solution for the 2D Linear Fredholm Functional Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Neda Khaksari ◽  
Mahmoud Paripour ◽  
Nasrin Karamikabir
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Unknown Function ◽  
Numerical Solutions ◽  
Functional Integral ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.

On the Theory of Linear Integral Equations

1935 ◽  
Vol 31 (1) ◽  
pp. 76-84 ◽  
Author(s):  
F. Smithies
Keyword(s):  
Special Reference ◽  
Integral Equations ◽  
Volterra Type ◽  
Linear Integral ◽  
Linear Integral Equations

The object of this paper is to extend the ordinary theory of integral equations of the second kind to certain classes of more general kernels and functions, with special reference to equations of the Volterra type.

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