In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t)+ a(t)ẋ(t)+ b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t)+ ∫ t t0 e ∫ t s a(ξ)dξb(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived. © 2010 Elsevier Ltd. All rights reserved.

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence solves a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accurac...

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence solves a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accurac...

An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction A + A → ∅ modeling is discussed. Finite difference method together with the linear approximation of the unknown function is considered. For divergent integrals presented in the equation for dimension d = 2 a regularization is used. Some numerical results are p...

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...

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. T...

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence solves a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accurac...

We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness of generalized stochastic flows. Moreover, we also prove the existence and uniqueness of L-solutions or measure-valued solutions for second order integro-differential equation of Fokker-Planck type.

The initial-value problem for a class of Volterra functional differential equations— of sufficient generality to encompass, as special cases, ordinary differential equations, retarded differential equations, integro-differential equations, and hysteretic differential equations— is studied. A self-contained and elementary treatment of this over-arching problem is provided, in which a unifying th...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...