3 research outputs found
Numerical solutions of the generalized equal width wave equation using the Petrov–Galerkin method
In this article, we consider a generalized equal width wave (GEW) equation
which is a significant nonlinear wave equation as it can be used to model many problems occurring in applied sciences. Here we study a Petrov–Galerkin method for the model problem, in which element shape functions are quadratic and weight functions are linear B-splines. We investigate the existence and uniqueness of solutions of the weak form of the
equation. Then, we establish the theoretical bound of the error in the
semi-discrete spatial scheme as well as of a full discrete scheme at t = t
n.
Furthermore, a powerful Fourier analysis has been applied to show that the
proposed scheme is unconditionally stable. Finally, propagation of solitary
waves and evolution of solitons are analyzed to demonstrate the efficiency
and applicability of the proposed scheme. The three invariants (I1, I2 and I3)
of motion have been commented to verify the conservation features of the
proposed algorithms. Our proposed numerical scheme has been compared
with other published schemes and demonstrated to be valid, effective and
it outperforms the others