An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications

NDATAH IDARA UDOH | 61 pages (10676 words) | Theses

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.

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APA

NDATAH, U (2021). An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications. Mouau.afribary.org: Retrieved Dec 23, 2024, from https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2

MLA 8th

UDOH, NDATAH. "An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications" Mouau.afribary.org. Mouau.afribary.org, 16 Jul. 2021, https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2. Accessed 23 Dec. 2024.

MLA7

UDOH, NDATAH. "An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications". Mouau.afribary.org, Mouau.afribary.org, 16 Jul. 2021. Web. 23 Dec. 2024. < https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2 >.

Chicago

UDOH, NDATAH. "An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications" Mouau.afribary.org (2021). Accessed 23 Dec. 2024. https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2

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