scholarly journals Fredholm-Volterra integral equation with potential kernel

2001 ◽  
Vol 26 (6) ◽  
pp. 321-330
Author(s):  
M. A. Abdou ◽  
A. A. El-Bary
Keyword(s):  
Integral Equation ◽  
Continuous Function ◽  
Volterra Integral Equation ◽  
Fredholm Integral Equation ◽  
Integral Term ◽  
Potential Kernel ◽  
Generalized Potential ◽  
Potential Form

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the spaceL2(Ω)×C(0,T),Ω={(x,y):x2+y2≤a},z=0, andT<∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the classC([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the classC[0,T]. Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established in the paper.

scholarly journals An asymptotic model for solving mixed integral equation in some domains

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Mohamed Abdella Abdou ◽  
Hamed Kamal Awad
Keyword(s):  
Integral Equation ◽  
Potential Function ◽  
Theory Of Elasticity ◽  
Asymptotic Model ◽  
Logarithmic Function ◽  
Integral Term ◽  
Special Cases ◽  
Generalized Potential ◽  
Carleman Function ◽  
Axisymmetric Problems

Abstract In this paper, we discuss the solution of mixed integral equation with generalized potential function in position and the kernel of Volterra integral term in time. The solution will be discussed in the space $$L_{2} (\Omega ) \times C[0,T],$$ L 2 ( Ω ) × C [ 0 , T ] , $$0 \le t \le T < 1$$ 0 ≤ t ≤ T < 1 , where $$\Omega$$ Ω is the domain of position and $$t$$ t is the time. The mixed integral equation is established from the axisymmetric problems in the theory of elasticity. Many special cases when kernel takes the potential function, Carleman function, the elliptic function and logarithmic function will be established.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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