Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations

Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations

In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...

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...

Operator-splitting Methods Respecting Eigenvalue Problems for Convection-diffusion and Wave Equations

We discuss iterative operator-splitting methods for convection-diffusion and wave equations motivated from the eigenvalue problem to decide the splitting process. The operator-splitting methods are well-know to solve such complicated multi-dimensional and multi-physical problems. Often the problem, how to decouple the underlying operators, is not understood well enough. We propose a method base...

Corrected Operator Splitting for Nonlinear Parabolic Equations

We present a corrected operator splitting (COS) method for solving nonlinear parabolic equations of convection-diiusion type. The main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps, as opposed to standard operator splitting (OS) which fails to do so. COS is based on solving a conservation law for modeling convection, a heat type equation ...

Operator splitting for partial differential equations with Burgers nonlinearity