On a discussion of Volterra–Fredholm integral equation with discontinuous kernel

Fredholm-volterra Integral Equation with Potential Kernel

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

On the Volterra Integral Equation with Weakly Singular Kernel

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...

Integral Equation Methods for the Inverse Problem with Discontinuous Wavespeed

The recovery of the coe cient H(x) in the one-dimensional generalized Schrodinger equation d =dx + kH(x) = Q(x) ; where H(x) is a positive, piecewise continuous function with positive limits H as x ! 1; is studied. The large-k asymptotics of the wavefunctions and the scattering coe cients are analyzed. A factorization formula is given expressing the total scattering matrix as a product of simp...

Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel

M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, On the numerical solutions of Fredholm-Volterra integral equation, Appl. Math. Comp. 146, 713-728, (2003). M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, Toeplitz Matrix and product Nystrom methods for solving the singular integral equation, Le Matematiche LVII-Fasc. I, 21-37, (2002). H. Brunner, On the numerical solution of nonlinear VolterraF...