The study of the stability of solutions to differential
equations is a fundamental and ongoing area of research in mathematics and
applied sciences with numerous applications, and it provides a framework for
analysing the behaviour of dynamical systems and predicting their long-term
behaviour. For a numerical solution to be useful it must be both consistent and
stable, and such a solution can be said to be stable if small errors in the
initial data or in the numerical approximation do not grow unbounded as the
computations progresses. In this paper, the stability of finite difference
methods for time-dependent Schrodinger equation with Dirichlet boundary
conditions on a staggered mesh was considered with explicit and implicit
discretization. It is demonstrated that the solution is conditionally stable
for the explicit finite difference technique and unconditionally stable for the
implicit finite difference methods using the numerical algorithm's matrix
representation. We will utilize a 1D harmonic oscillator problem to demonstrate
this behaviour.
Author(s)details:-
Dr. Ohwadua, E.O.
Department of Mathematical Sciences, Bingham University, Nasarawa State,
Nigeria.
Please See the book
here :- https://doi.org/10.9734/bpi/rumcs/v6/203
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