Method of upper and lower solutions and interval method for semilinear Euler-Poisson-Darboux equations

Differential Equations and the Method of Upper and Lower Solutions

The purpose of this paper is to give an exposition of the method of upper and lower solutions and its usefulness to the study of periodic solutions to differential equations. Some fundamental topics from analysis, such as continuity, differentiation, integration, and uniform convergence, are assumed to be known by the reader. Concepts behind differential equations, initial value problems, and b...

Lower-Upper Symmetric-Gauss-Seidel Method for the Euler and Navier-Stokes Equations

A NEW multigrid relaxation scheme is developed for the steady-state solution of the Euler and Navier-Stokes equations. The lower-upper Symmetric-Gauss-Seidel method (LUSGS) does not require flux splitting for approximate Newton iteration. The present method, which is vectorizable and unconditionally stable, needs only scalar diagonal inversions. Application to transonic flow shows that the new ...

The method of lower and upper solutions for fourth order equations with the Navier condition

The Method of Lower and Upper Solutions for Some Fourth-order Equations

In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eige...

semi-analytical solution for static and forced vibration problems of laminated beams through smooth fundamental functions method

در این پایان نامه روش جدیدی مبتنی بر روش حل معادلات دیفرانسیل پارهای بر اساس روش توابع پایه برای حل مسایل ارتعاش اجباری واستاتیک تیرها و صفحات لایه ای ارایه شده است که می توان تفاوت این روش با روش های متداول توابع پایه را در استفاده از توابع هموار در ارضاء معادلات حاکم و شرایط مرزی دانست. در روش ارایه شده در این پایاننامه از معادله تعادل به عنوان معادله حاکم بر رفتار سیستم استفاده شده است که مو...