1,582 research outputs found
Numerical solution of the modified equal width wave equation
Numerical solution of the modified equal width wave equation is obtained by using lumped
Galerkin method based on cubic B-spline finite element method. Solitary wave motion and
interaction of two solitary waves are studied using the proposed method. Accuracy of the
proposed method is discussed by computing the numerical conserved laws L2 and L∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated
Petrov galerkin method with cubic B splines for solving the MEW equation
In the present paper, we introduce a numerical solution algorithm based
on a Petrov-Galerkin method in which the element shape functions are cubic
B-splines and the weight functions quadratic B-splines . The motion of a single
solitarywave and interaction of two solitarywaves are studied. Accuracy
and efficiency of the proposed method are discussed by computing the numerical
conserved laws and L2 , L¥ error norms. The obtained results show
that the present method is a remarkably successful numerical technique for
solving the modified equal width wave(MEW) equation. A linear stability
analysis of the scheme shows that it is unconditionally stable
Numerical investigations of shallow water waves via generalized equal width (GEW) equation
In this article, a mathematical model representing solution of the nonlinear generalized
equal width (GEW) equation has been considered. Here we aim to investigate solutions
of GEW equation using a numerical scheme by using sextic B-spline Subdomain finite
element method. At first Galerkin finite element method is proposed and a priori bound
has been established. Then a semi-discrete and a Crank-Nicolson Galerkin finite element
approximation have been studied respectively. In addition to that a powerful Fourier series
analysis has been performed and indicated that our method is unconditionally stable.
Finally, proficiency and practicality of the method have been demonstrated by illustrating it
on two important problems of the GEW equation including propagation of single solitons
and collision of double solitary waves. The performance of the numerical algorithm has
been demonstrated for the motion of single soliton by computing L∞ and L2 norms and
for the other problem computing three invariant quantities I1, I2 and I3. The presented
numerical algorithm has been compared with other established schemes and it is observed that the presented scheme is shown to be effectual and valid
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
Structures and waves in a nonlinear heat-conducting medium
The paper is an overview of the main contributions of a Bulgarian team of
researchers to the problem of finding the possible structures and waves in the
open nonlinear heat conducting medium, described by a reaction-diffusion
equation. Being posed and actively worked out by the Russian school of A. A.
Samarskii and S.P. Kurdyumov since the seventies of the last century, this
problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer
Proceedings in Mathematics and Statistics, Numerical Methods for PDEs:
Theory, Algorithms and their Application
Embedded discontinuous Galerkin transport schemes with localised limiters
Motivated by finite element spaces used for representation of temperature in
the compatible finite element approach for numerical weather prediction, we
introduce locally bounded transport schemes for (partially-)continuous finite
element spaces. The underlying high-order transport scheme is constructed by
injecting the partially-continuous field into an embedding discontinuous finite
element space, applying a stable upwind discontinuous Galerkin (DG) scheme, and
projecting back into the partially-continuous space; we call this an embedded
DG scheme. We prove that this scheme is stable in L2 provided that the
underlying upwind DG scheme is. We then provide a framework for applying
limiters for embedded DG transport schemes. Standard DG limiters are applied
during the underlying DG scheme. We introduce a new localised form of
element-based flux-correction which we apply to limiting the projection back
into the partially-continuous space, so that the whole transport scheme is
bounded. We provide details in the specific case of tensor-product finite
element spaces on wedge elements that are discontinuous P1/Q1 in the horizontal
and continuous P2 in the vertical. The framework is illustrated with numerical
tests
Subdomain finite element method with quartic B-splines for the modified equal width wave equation
In this paper, a numerical solution of the modified equal width wave (MEW) equation, has
been obtained by a numerical technique based on Subdomain finite element method with quartic Bsplines. Test problems including the motion of a single solitary wave and interaction of two solitary waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L2 and L∞. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable
A numerical solution of the MEW equaiton using sextic B splines
In this article, a numerical solution of the modified equal width wave
(MEW) equation, based on subdomain method using sextic B-spline is used to simulate the motion of single solitary wave and interaction of two solitary waves. The three
invariants of the motion are calculated to determine the conservation properties of the
system. L2 and L∞ error norms are used to measure differences between the analytical and numerical solutions. The obtained results are compared with some published
numerical solutions. A linear stability analysis of the scheme is also investigate
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