Iteration procedures for the Dirichlet difference problem

Iteration Procedures for the Dirichlet Difference Problem

Introduction. A fundamental paper in the theory of solving partial differential equations by iteration has been written by Frankel.1 In this paper Frankel discusses the Richardson and Liebmann procedures and their corresponding accelerated procedures. The latter are termed the extrapolated Liebmann and the second-order Richardson procedures. From his paper three disadvantages of the second-orde...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The Dirichlet Problem for a Class of Elliptic Difference Equations

Under suitable assumptions on the order of nonlinearity we prove existence and uniqueness theorems for difference Dirichlet problems of divergence type. We also show that the discrete solutions converge to a solution of the continuous problem. We do not assume that our equation comes from a variational problem. Some of our results are constructive or allow for the application of constructive me...

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

On the Numerical Solution of the Dirichlet Problem for Laplace's Difference Equation*