Results 171 to 180 of about 7,526 (199)

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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gu, Zhendong, Guo, Xiaojing, Sun, Daochun   +2 more
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Superconvergence of Numerical Solutions to Volterra Integral Equations with Singularities

SIAM Journal on Numerical Analysis, 1997
The paper is devoted to the collocation method for weakly singular Volterra integral equations \[ x(t)+ \int^t_0 (t-s)^{-\alpha} h(t,s)x(s)ds= f(t),\quad t\in J=[0,T],\tag{1} \] with ...
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System of nonlinear Volterra’s integral equations with polar kernel and singularities

Nonlinear Analysis: Theory, Methods & Applications, 2007
Using one special Colombeau algebra and the method of regularization of fractional derivatives with a delta sequence, the author proves the existence and the uniqueness of the solution of a system of nonlinear Volterra integral equations with polar kernel.
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A class of singularly perturbed singular Volterra integral equations

Asymptotic Analysis, 2000
A uniformly valid asymptotic expansion is established for the solution to certain singularly perturbed generalized Abel integral equations. The results are applied to a problem in heat conduction.
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Volterra Type Integral Equation with Super-Singular Kernels

2017
In this work we suggest a new method for investigating the model Volterra type integral equation with super-singularity, the kernel of which consists of a composition of polynomial functions with super-singularity and functions with super-singular points.
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