Chapter 5

Chapter 4 Elliptic Equations

Tadeusz Stys

Abstract

In chapter 4, two finite difference schemes are built for Helmholtz equation with Dirich- let’s boundary value conditions. It is proved that the first scheme is O(h2 1 + h2 2) convergent in the norm of the Hilbert’s space H and in the maximum norm. The second scheme is O(h4 1 + h4 2 ) accurate and is also convergent in the norm of the Hilbert’s space H and in the maximum norm. Both schemes are solved by the Mathematica module. In the last section, Poisson’s equation with Dirichlet’s boundary conditions is solved by the method of lines. The chapter ends with a set of questions.

Total Pages: 78-99 (22)

Purchase Chapter  Book Details

RELATED BOOKS

.Advanced Mathematical Applications in Data Science.
.Markov Chain Process (Theory and Cases).
.Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering.
.On Generalized Growth rates of Integer Translated Entire and Meromorphic Functions.