Abstract: The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential...

We study some stability criteria in terms of two measures for setvalued perturbed hybrid integro-differential equations of mixed type with fixed moments of impulse. Stability properties of perturbed system are obtained via a comparison result which connects the solutions of perturbed system and the unperturbed one through the solutions of a comparison system. AMS (MOS) Subject Classification. 3...

In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good properties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numerical results are given to show the efficiency of...

Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations.  2003 Elsevier Science (USA). All rights reserved.

The main purpose of this paper is to consider Adomian's decomposition method in non-linear Volterra integro-differential equations. The advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of Adomian's method applied to such nonlinear integro-differential equations are discussed. Finally, by ...

When underlying financial variables follow a Markov jump-diffusion process, the value function of a derivative security satisfies a partial integro-differential equation (PIDE) for European-style exercise or a partial integro-differential variational inequality (PIDVI) for American-style exercise. Unless the Markov process has a special structure, analytical solutions are generally not availabl...

The model recently proposed in Ref.1 is used to derive linear integro– differential equations whose solutions provide reasonable estimates for the momentum distribution and condensate fraction in interacting many–boson system at zero temperature. An advantage of these equations is that they can be employed in the weak coupling regime and beyond. As an example, analytical treatment of the weak c...

In this paper we present an automated proof for the confluence of a rewrite system for integro-differential operators (given in Table 1). We also outline a generic prototype implementation of the integro-differential polynomials—the key tool for this proof—realized using the Theorema system. With its generic functor mechanism—detailed in Section 2—we are able to provide a formalization of the t...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...