Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations

An efficient technique for solving parabolic partial integrodifferential equation is presented. This technique is based on Chebyshev polynomials and finite difference method.A priorierror estimate for the proposed technique is deduced. Some examples are presented to illustrate the validity and efficiency of the presented method.

Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.

Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.

Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.

On Some Nonlinear Integrodifferential Inequalities for Functions of Independent Variables

The object of this paper is to establish some nonlinear integrodifferential integral inequalities in independent variables. These new inequalities represent a generalization of the results obtained by Pachpatte in the case of a function with one and two variables. Our results can be used as tools in the qualitative theory of a certain class of partial integrodifferential equation.