Results 171 to 180 of about 14,005 (202)

Collocation methods for nonlinear stochastic Volterra integral equations

Computational and Applied Mathematics, 2020
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Xiaoli Xu, Yu Xiao, Haiying Zhang
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On a Nonlinear Volterra Integral Equation on a Hilbert Space

SIAM Journal on Mathematical Analysis, 1977
Nonlinear Volterra integral equations with singular kernels are considered. The existence and the asymptotic behavior of solutions is studied in a special case.
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APPROXIMATE SOLUTIONS OF NONLINEAR VOLTERRA INTEGRAL EQUATION SYSTEMS

International Journal of Modern Physics B, 2010
The purpose of this study is to implement a new approximate method for solving system of nonlinear Volterra integral equations. The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation ...
Yalçinbaş, Salih, Erdem, Kübra
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Nonlinear Volterra Integral Equations

2011
It is well known that linear and nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics, and semi-conductor devices. Volterra started working on integral equations in 1884, but his serious study began in 1896. The name integral equation was given by du Bois-Reymond in 1888.
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Asymptotic Solutions of Some Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1981
The asymptotic behavior of solutions of three nonlinear Volterra integral equations of the form $u(t) + \int_0^t {A(t - s)g(u(s))ds = 0} $ is studied. These equations arise from certain diffusion problems, in dimensions 1, 2 or 3, with nonlinear boundary conditions.
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On a class of nonlinear Volterra-Fredholm q-integral equations

Fractional Calculus and Applied Analysis, 2013
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ON OPTIMAL CONTROL FOR NONLINEAR VOLTERRA-STIELTJES INTEGRAL EQUATIONS

IFAC Proceedings Volumes, 1983
Abstract Some results concerning the optimal control for measure differ-ential equations are generalized to the case of Volterra equations. Because of a suitable non-anticipative version of the underlying system equation, already the usual Lipschitz condition guarantees the existence of a unique solution.
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Nonlinear stability of direct quadrature methods for Volterra integral equations

Mathematics and Computers in Simulation, 2015
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MESSINA, ELEONORA, A. Vecchio
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Representation of exact solution for the nonlinear Volterra–Fredholm integral equations

Applied Mathematics and Computation, 2006
This paper is concerned with the existence of the exact solution of the following nonlinear Volterra-Fredholm integral equation \[ u(x)=f(x)+Gu(x), \] where \[ Gu(x)=\lambda_{1}\int_{a}^{x}K_{1}(x,\xi)N_{1}(u(\xi))\,d\xi +\lambda_{2}\int_{a}^{b}K_{2}(x,\xi)N_{2}(u(\xi))\,d\xi, \] \(u(x)\) is the unknown function, \(u(x), \;f(x)\in W^{1}_{2}[a,b], \;N_ ...
Minggen Cui, Hong Du
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Stability Considerations for a Volterra Integral Equation with Discontinuous Nonlinearity

SIAM Journal on Control, 1973
The asymptotic behavior of the solutions of a Volterra integral equation with discontinuous nonlinearity is investigated. The global existence of solutions is proved and some sufficient conditions for local and/or global stability are obtained by means of the Popov-type method.
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