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Full-Text Articles in Mathematics

A Modified Crank-Nicolson Method, Ernest David Jordan Jr. Jan 1981

A Modified Crank-Nicolson Method, Ernest David Jordan Jr.

Theses and Dissertations

In order to obtain a numerical solution to the heat equation using finite differences, either implicit or explicit equations are used to formulate a solution. The advantage in an explicit formulation is its simplicity and minimal computer storage requirements while its disadvantage is its instability. The opposite is true for an implicit formulation such as the Crank-Nicolson method; although it is stable it is more difficult to implement and requires a much larger memory capacity. In this paper we examine the accuracy and stability of a hybrid approach, a modified Crank-Nicolson formulation, that combines the advantageous features of both the …


Calculation Of Galois Groups, Daniel Schnackenberg May 1978

Calculation Of Galois Groups, Daniel Schnackenberg

Theses and Dissertations

In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory and some useful facts about factorization, I develop the important methods of calculating the Galois group and give a proof of the Chebotarev density theorem.