On the splitting-up method and stochastic partial differential equations

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Splitting up method for the 2D stochastic Navier-Stokes equations

Abstract. In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the LieTrotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given either with per...

Stochastic Partial Differential Equations

Convergence Analysis of a Splitting Method for Stochastic Differential Equations

(1) { dy(t) = f(y(t))dt + g(y(t))dW (t), 0 ≤ t ≤ T y(0) = y0 where T > 0 is the terminal time, y(t) : [0, T ]× Ω → R, f(y) : R → R, g(y) : R → Rm×d, and W (t) = (W1(t), · · · ,Wd(t))∗ is a standard d-dimensional Brownian motion defined on a complete, filtered probability space (Ω,F , P, {Ft}0≤t≤T ). Stochastic differential equations are used in many fields, such as stock market, financial mathe...

THE ELZAKI HOMOTOPY PERTURBATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...