| dc.description.abstract | The Kotteweg-de Vrr-es(KdV)is a mathematical model of waves on shallow
water surfaces. The mathematical theory behind the KdV equation
is rich and interesting, and, in the broad sense, is a topic of active mathematical
research. The equation is named after Diederik Korteweg and
Gustav de Vries,
It has long been known that conservative discretization schemes for
the KdV and other nonlinear equations tend to become numericrtlly unstable.
Although finite difference approximations have been used, there
are always instabilities of the solutions obtained,
In this work we solved the Korteweg-ds Vries (KdV) equation using an
explicit finite difference method, subject. to various boundery conditions
which are travelling wave solutions to the KdV equation. The methodology
involved carefully designing conservative finite difference discretization
that can remain stable and deliver sharp solution profiles fora long
time. We then determined the accuracy of the finite diffurence scheme by
comparing the graphical outputs of the numerical results. | en_US |
