Results 181 to 190 of about 3,600 (223)

Fredholm theory of Heitler’s integral equation

Acta Physica Academiae Scientiarum Hungaricae, 1954
The Fredholm theory of non-homogeneous integral equation has been applied to Heitler’s integral equation for radiation damping in scattering processes which are beset with divergence difficulties. The general convergence of the solution has been discussed, from the mathematical point of view.
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On Volterra-Fredholm integral equations

Periodica Mathematica Hungarica, 1993
The Ważewski method associated with the convergence of successive approximations is used in order to obtain existence and uniqueness results for the functional-integral equation of Volterra-Fredholm type of the form \[ \begin{multlined} x(t)=F \Biggl( t,x(t), \int_ 0^ t f_ 1(t,s,x(s))ds,\dots, \int_ 0^ t f_ n(t,s,x(s))ds,\\ \int_ 0^ T g_ 1(t,s,x(s))ds,\
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Fredholm systems of integral equations

Russian Mathematical Surveys, 1998
Let \(\Gamma\) and \(\gamma\) be disjoint sets of segments on the real axis, \(D=\Gamma\cup\gamma\). The author studies the integral equations \[ {1\over\pi}\int_\Gamma{\mu(\sigma)\over\sigma-s} d\sigma+\int_D\mu(\sigma) v(s,\sigma) d\sigma=f(s),\;s\in\Gamma, \] \[ \mu(s)+\int_D\mu(\sigma)w(s,\sigma) d\sigma=f(s),\;s\in\gamma, \] \[ \int_D\mu(\sigma ...
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Systems of Fredholm Integral Equations

2011
Systems of Volterra and Fredholm integral equations have attracted much concern in applied sciences. The systems of Fredholm integral equations appear in two kinds. The system of Fredholm integral equations of the first kind [1–5] reads $$\begin{gathered} {f_1}\left( x \right) = \int_a^b {\left( {{K_1}\left( {x,t} \right)u\left( t \right ...
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On nonlinear Fredholm–Volterra integral equations with hysteresis

Applied Mathematics and Computation, 2004
The author improves his earlier result concerning the existence and uniqueness of solutions of the following Fredholm-Volterra system with hysteresis \[ x(t)= g(t)+ \int^t_0 p(t,s)\phi(s, x(s), w[S[x]](s))\,ds+ \int^\infty_0 q(t,s) \psi(s, x(s), w[S[x]](s))\,ds,\tag{1} \] where \(w\) denotes a hysteresis operator and \(S\) is the superposition operator
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Numerical methods for Fredholm integral equations on the square

Applied Mathematics and Computation, 2011
The paper is devoted to the construction and investigation of numerical methods for two-dimensional Fredholm integral equations on a square. The problem is considered in a weighted setting, allowing the given functions and the unknown solutions to have weak singularities at the boundaries of the fundamental domain. Two concrete approaches are followed,
Donatella Occorsio, Maria Grazia Russo
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Estimates for fredholm integral equations

Numerical Functional Analysis and Optimization, 1999
There would seem to exist a lack of a priori estimates for the solutions of Fredholm integral equations. This article provides a constructive method to determine bounds on the solution of linear second kind Fredholm equations. To this aim a given Fredholm equation isreformulated as an equivalent problem with a positive kernel.
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Generalized Fredholm Integral Equations

2016
In this chapter we adapt the Adomian decomposition method, the modified decomposition method, the noise term phenomenon, the direct computation method and the successive approximation method for generalized Fredholm integral equations.
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Volterra-Fredholm Integral Equations

2011
The Volterra-Fredholm integral equations [1–2] arise from parabolic boundary value problems, from the mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and biological models. The Volterra-Fredholm integral equations appear in the literature in two forms, namely $$u\left( x \right) = f\left( x \right)
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Fredholm Integral Equations

2021
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