Results 71 to 80 of about 466,993 (231)
Solutions for singular Volterra integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We consider the system of Volterra integral equations $$ \begin{array}{l} u_i(t)=\int_{0}^{t}g_i(t,s)[P_i(s,u_1(s),u_2(s),\cdots, u_n(s)) + Q_i(s,u_1(s),u_2(s),\cdots, u_n(s))]ds, t\in [0,T],1\leq i\leq n \end{array} $$ where $T>0$ is fixed and the nonlinearities $P_i(t,u_1,u_2,\cdots,u_n)$ can be singular at $t=0$ and $u_j=0$ where $j\in\{1,2,\cdots,n\
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Applications of Normal S-Iterative Method to a Nonlinear Integral Equation
The Scientific World Journal, 2014 It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.
Faik Gürsoy
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Numerical Methods of Optimal Accuracy for Weakly Singular Volterra Integral Equations [PDF]
arXiv, 2013 Weakly singular Volterra integral equations of the different types are considered. The construction of accuracy-optimal numerical methods for one-dimensional and multidimensional equations is discussed. Since this question is closely related with the optimal approximation problem, the orders of the Babenko and Kolmogorov \(n-\)widths of compact sets ...
arxiv
Itô differential representation of singular stochastic Volterra integral equations [PDF]
arXiv, 2020 In this paper we obtain an It\^o differential representation for a class of singular stochastic Volterra integral equations. As an application, we investigate the rate of convergence in the small time central limit theorem for the solution.
arxiv
Volterra Equations Driven by Rough Signals [PDF]
arXiv, 2019 This article is devoted to the extension of the theory of rough paths in the context of Volterra equations with possibly singular kernels. We begin to describe a class of two parameter functions defined on the simplex called Volterra paths. These paths are used to construct a so-called Volterra-signature, analogously to the signature used in Lyon's ...
arxiv
On Hyers-Ulam-Rassias stability of a Volterra-Hammerstein functional integral equation [PDF]
arXiv, 2020 The aim of this paper is to study Hyers-Ulam-Rassias stability for a Volterra-Hammerstein functional integral equation in three variables via Picard operators.
arxiv
On Monotonic and Nonnegative Solutions of a Nonlinear Volterra-Stieltjes Integral Equation
Journal of Function Spaces, 2014 We study the existence of monotonic and nonnegative solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous on a bounded interval. The main tools used in our considerations are the technique
Tomasz Zając
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Integral equations for the wave function of particle systems
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2019 Constructions of integral equations to the wave function of particle systems in bound state have been proposed in this work. We obtain the kernel of the Fredholm type integral equation for an odd number of particles in explicit form. Besides, an integral
K.V. Avdonin
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The Asymptotic Behavior of Solutions of Systems of Volterra Integral Equations [PDF]
, 1948 Alfred Horn
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