Results 131 to 140 of about 307 (168)

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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On Volterra Type Singular Integral Equations

Georgian Mathematical Journal, 2001
Conditions for the boundedness are established, and the norms of Volterra type one-dimensional integral operators with fixed singularities of first order in the kernel are calculated in the space L2 with weight. Integral equations of second order, containing the said operators, are investigated.
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Numerical solution of Volterra integral equations with singularities

Frontiers of Mathematics in China, 2013
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Kolk, Marek, Pedas, Arvet
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The Numerical Solution of Singular Volterra Integral Equations

SIAM Journal on Numerical Analysis, 1968
It is possible to prove by Laplace transform analysis that (1.1) has a unique solution R(t) satisfying the foregoing conditions. However, this approach is not very useful for numerical purposes. We shall present a practical and efficient method of approximate solution. The successive approximations are piecewise linear.
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Numerical methods for nonlinear singular Volterra integral equations

AIP Conference Proceedings, 2012
This work is concerned with the numerical solution of two related nonlinear singular Volterra integral equations which arise in connection with a heat transfer problem. We consider product integration and collocation methods for both equations and several numerical results are presented illustrating the performance of these methods.
Teresa Diogo, Magda Rebelo
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Parallel methods for weakly singular Volterra integral equations on GPUs

Applied Numerical Mathematics, 2017
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CONTE, Dajana, PATERNOSTER, Beatrice
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Fredholm-Volterra integral equation with singular kernel

Korean Journal of Computational and Applied Mathematics, 1999
The paper deals with the numerical solution of Fredholm-Volterra integral equations with Carleman kernel in the space \(L_2(-1,1)\times C(0,T)\), \(0\leq t\leq ...
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Systems of Fredholm and Volterra Integral Equations: Integrable Singularities

2013
In this chapter we consider three systems of singular integral equations. Specifically we are interested in the following systems of Fredholm integral equations $$\displaystyle{ u_{i}(t) =\int _{ 0}^{1}g_{ i}(t,s)f_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$ (7.1.1) $$\displaystyle{ u_{i}(t) =\int _{
Ravi P. Agarwal, Donal O’Regan, Patricia J. Y. Wong   +2 more
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Some Classes of Nonlinear Mixed Volterra and Singular Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1992
Existence theorems for some classes of nonlinear mixed Volterra and singular integral or integro-differential equations are proved applying methods of monotone operator theory and Schauder’s fixed point theorem, respectively. Moreover, uniqueness theorems for the solution are given.
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Series expansion method for weakly singular Volterra integral equations

Applied Numerical Mathematics, 2016
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Gu, Zhendong, Guo, Xiaojing, Sun, Daochun   +2 more
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