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...

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. ...

In this paper stability inequalities for the linear nonhomogeneous Volterra delay integro-differential equation (VDIDE) is being established. The particular problems are encountered to show applicability of method and confirm predicted theoretical analysis.

The aim of this work is to revisit viscosity solutions’ theory for second-order elliptic integrodifferential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen-Ishii’s Lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The pr...

Abstract In this paper, a new form of the homotopy perturbation method (NHPM) has been adopted for solving integro-differential equations. In the present study, firstly the NHPM is used to the integro-differential equation, which yields the Maclaurin series of the exact solution. By applying the Laplace transformation to the truncated Maclaurin series and then the Padé approximation to the solu...