We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler scheme...

A numerical method is presented to solve a two-dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion. Since direct solutions based on implicit schemes for multidimensional problems are computa-tionally inefficient, we apply an alternating direction method which is second order accurate in time and space. The stability of the...

Milstein and approximate coupling approaches are compared for the pathwise numerical solutions to stochastic differential equations (SDE) driven by Brownian motion. These methods attain an order one convergence under nondegeneracy assumption of diffusion term method. We use MATLAB simulate these applying them a particular two-dimensional SDE. Then, we analyze performance both amount time requir...

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework consid...

In typical stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using Itô’s formula, we get rid, in the asset price dynamics, of the stochastic integral with respect to the Brownian motion driving this SDE. Taking advant...

This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...