An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications

ABSTRACT

This research work demonstrates the importance of tridiagonal matrices and their applications to the solution of differential equations in general. An example of a system of coupled oscillators is given by an ordinary differential equation; a number of useful lemmas will be proven to establish the validity of our approach. An example to show how tridiagonal matrices arise naturally in the dynamics of coupled systems involving n equal masses attached to a string equidistant from each other is considered. An efficient computer-aided designed program for computing the inverse of any tridiagonal matrix is presented, a two-point boundary-value problem which describes the steady state phenomenon of temperature distribution in a rod is also considered and the governing equation of this boundary value problem is discretized using central differences. A second order nonlinear equation is also solved using the Newton's iterative scheme.the numerical solutions is obtained by implementing the MathCAD inversion algorithm; and results in both cases are analyzed.