Piecewise-linearized and linearized θ-methods for ordinary and partial differential equations

Solving Initial Value Problems for Ordinary Differential Equations by two approaches: BDF and piecewise-linearized methods

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...

PML - methods for the linearized Euler equations

A recently suggested method for absorbing boundary conditions for the Euler equations is examined. The method is of PML type and has the important property of being well posed. Results from numerical experiments using a second order discretization are presented. For some choices of parameters the method becomes unstable. The instability is observed to originate from the corner regions. A modifi...

Differential Constraints Compatible with Linearized Equations

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints. One of the standard ways for determining particular solutions to partial differential equations is to reduce them to ordinary differential equations which are easier to solve. The classical work of Lie abo...

Piecewise-linearized methods for initial-value problems with oscillating solutions

Two piecewise-linearized methods for the numerical solution of nonlinear second-order differential equations which contain the first-order derivative are presented. These methods provide piecewise analytical solutions in open intervals, result in explicit finite difference equations for both the displacement and the velocity or only the displacement, at nodal points, and continuous solutions ev...