Results 181 to 190 of about 3,512 (232)

Fredholm Integral Equations

2011
It was stated in Chapter 2 that Fredholm integral equations arise in many scientific applications. It was also shown that Fredholm integral equations can be derived from boundary value problems. Erik Ivar Fredholm (1866– 1927) is best remembered for his work on integral equations and spectral theory. Fredholm was a Swedish mathematician who established
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Fredholm–Volterra integral equation in contact problem

Applied Mathematics and Computation, 2003
The author considers the Fredholm-Volterra integral equation \[ kP(x,y,t)+q\int\limits_0^\infty\int\limits_0^\infty \frac{P(\xi,\eta,t)\,d\xi\,d\eta}{\sqrt{(x-\xi)^2+(y-\eta)^2}} +q\int\limits_0^t F(t,\tau)P(x,y,\tau) \,d\tau=f(x,y,t) \tag{1} \] in the space \(L_2(\Omega)\times C(0,T)\), under the condition \[ \int\limits_0^\infty\int\limits_0^\infty P(
Abdou, M. A., Moustafa, Osama L.
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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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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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Nonlinear Fredholm Integral Equations

2011
It was stated in Chapter 4 that Fredholm integral equations arise in many scientific applications. It was also shown that Fredholm integral equations can be derived from boundary value problems. Erik Ivar Fredholm (1866–1927) is best remembered for his work on integral equations and spectral theory.
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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 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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Optimal Control of Nonlinear Fredholm Integral Equations

Journal of Optimization Theory and Applications, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fredholm–Volterra integral equation with singular kernel

Applied Mathematics and Computation, 2003
The author considers the Fredholm-Volterra integral equation of the second kind \[ \delta\phi(x,t)+\int\limits_{-1}^1 \left| \ln| y-x| -d\right| \phi(y,t)\,dy+\int\limits_0^t F(\tau)\phi(x,\tau) \,d\tau=f(x,t),\tag{1} \] where \(| x| \leq1,\) \( t\in[0,T],\) \(\lambda\in(0,\infty),\) \(\delta\in(0,\infty]\), with a specific right-hand side \(f(x,t ...
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