This paper considers investment problems in real options with non-homogeneous two-factor uncertainty. We derive some analytical properties of the resulting optimal stopping problem and present a finite difference algorithm to approximate firm’s value function exercise boundary. An important message our is that frequently applied quasi-analytical approach underestimates impact caused by fact sol...

We consider classical host-parasite systems consisting of ordinary differential equations for the total numbers of hosts, parasites,and larvae. We also consider a newer, spatially structured model that consists of a partial differential equation for each of those populations. We finally compare the behavior of solutions for the spatially homogeneous model to that of the solutions for the spatia...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential eq...

In this paper, the general solution of steady-state two-dimensional non-axisymmetric mechanical and thermal stresses and mechanical displacements of a hollow thick cylinder made of fluid-saturated functionally graded porous material (FGPM) is presented. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to sol...

We derive a lower bound on the large-time exponential behavior of the solution to a stochastic parabolic partial differential equation on R+ × R in the case of a spatially homogeneous Gaussian potential that is white-noise in time, and study the relation between the lower bound and the potential’s spatial modulus of continuity.

In this paper, we apply the homotopy perturbation method (HPM) for solving the Cauchy problems of the first-order partial differential equation. We obtain the exact solutions to the homogeneous or inhomogeneous linear and nonlinear equations. Numerical results are presented to confirm the efficiency of the HPM. Mathematics Subject Classification: 35K15, 35C05, 65D99, 65M99