We study the numerical approximation of viscosity solutions for Parabolic Integro-Differential Equations (PIDE). Similar models arise in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference ...

We consider the harvest of a certain proportion of a population that is modeled by an integro-difference equation. This model is discrete in time and continuous in the space variable. The dispersal of the population is modeled by an integral of the population density against a kernel function. The control is the harvest, and the goal is to maximize the profit. The optimal control is characteriz...

We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with statedependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and as...

We propose a site site generalization of the Lovett-Mow-Buff-Wertheim integro-differential equation for the one-particle density distributions to polyatomic fluids. The method provides microscopic description of liquid interfaces of molecular fluids and solutions. It uses the inhomogeneous site-site direct correlation function of molecular fluid consistently constructed by nonlinear interpolati...

An implicit-explicit Euler scheme in temporal direction is employed to discretize a partial integro-differential equation, which arises in pricing options under jumpdiffusion process. Then the semi-discretized equation is approximated in space by the Sinc-Galerkin method with exponential accuracy. Meanwhile, the domain decomposition method is incorporated to handle the non-smoothness of the pay...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...