Results 211 to 220 of about 25,245 (259)

A simplification to Fredholm’s solution to the Fredholm integral equation of the second kind

Applied Mathematics and Computation, 2007
The authors provide a simplification of the solution of a Fredholm integral equation of the second kind in terms of a ratio of determinants. Combinatorial arguments allow a major simplification of Fredholm's solution formula, economizing in particular on the number of multiple integrals to evaluate.
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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 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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Computation of the eigenvalues of Fredholm–Stieltjes integral equations

Applicable Analysis, 2006
The Rayleigh–Ritz and the inverse iteration methods are used in order to compute the eigenvalues of Fredholm–Stieltjes integral equations, i.e. Fredholm equations with respect to suitable Stieltjes-type measures. Some applications to the so-called ‘charged’ (in German ‘belastete’) integral equation, and particularly the problem of computing the ...
P. NATALINI, RICCI, Paolo Emilio
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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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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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On the numerical solutions of Fredholm–Volterra integral equation

Applied Mathematics and Computation, 2003
The authors describe the Toeplitz matrix method and the product Nystrom method for the mixed Fredholm-Volterra singular integral equation of the second kind: \[ \mu\phi(x,t)-\lambda\int_{-1}^1k(x,y)\phi(y,t)\,dy- \lambda\int_0^tF(t, \tau)\phi(x,\tau)\,d\tau= f(x,t),\quad 0\leqslant t\leqslant T,\;| x| \leqslant1,\tag{1} \] where \(k\), \(F\) and \(f ...
Abdou, M. A., Mohamed, Khamis I., Ismail, A. S.   +2 more
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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.
openaire   +1 more source