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.
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NDATAH, U (2021). An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications. Repository.mouau.edu.ng: Retrieved Nov 22, 2024, from https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2
UDOH, NDATAH. "An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications" Repository.mouau.edu.ng. Repository.mouau.edu.ng, 16 Jul. 2021, https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2. Accessed 22 Nov. 2024.
UDOH, NDATAH. "An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 16 Jul. 2021. Web. 22 Nov. 2024. < https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2 >.
UDOH, NDATAH. "An Algorithmic Approach To The Analysis Of Tridiagonal Matrices And Applications" Repository.mouau.edu.ng (2021). Accessed 22 Nov. 2024. https://repository.mouau.edu.ng/work/view/an-algorithmic-approach-to-the-analysis-of-tridiagonal-matrices-and-applications-7-2