In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

A proof of high-order convergence of three deterministic particle methods for the convectiondiffusion equation in two dimensions is presented. The methods are based on discretizations of an integro-differential equation in which an integral operator approximates the diffusion operator. The methods differ in the discretization of this operator. The conditions for convergence imposed on the kerne...

The expected discounted penalty with downside jumps has been extensively studied in Gerber and Shiu(1998), Gerber and Landry(1998), Tsai and Wilmott(2002) and others. In this paper, we study the expected discounted penalty in a perturbed compound Poisson model with two sided jumps. We show that it is always twice continuously differentiable provided that the jump size distribution has a bounded...

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra’s model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method redu...

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

In our symbolic approach to boundary problems for linear ordinary differential equations we use the algebra of integro-differential operators as an algebraic analogue of differential, integral and boundary operators (Section 2). They allow to express the problem statement (differential equation and boundary conditions) as well as the solution operator (an integral operator called “Green’s opera...

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equat...

Abstract We study the Volterra integro-differential equation on time scales and provide sufficient conditions for boundness of all solutions considered equation. Using that result, we present exponential stability All results proved general scale include both integral discrete equations.

Abstract. This paper presents new formulations of the boundary-domain integral equation (BDIE) and the boundary-domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equa...