Journal ArticleDOI
Numerical solutions of the regularized long-wave equation
Padam C. Jain,Labib Iskandar +1 more
TLDR
In this paper, the combined approach of quasilinearization and invariant imbedding is used for computing solutions of the nonlinear regularized long-wave (RLW) equation.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1979-11-01. It has received 34 citations till now. The article focuses on the topics: Benjamin–Bona–Mahony equation & Undular bore.read more
Citations
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Journal ArticleDOI
Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method
TL;DR: In this paper, the homotopy analysis method (HAM) is implemented for finding approximate solutions of the Burger and regularized long wave (RLW) equations, and the results of the proposed method are compared with the results obtained by HPM.
Journal ArticleDOI
Galerkin method for the numerical solution of the RLW equation using quintic B-splines
İdris Dağ,Bülent Saka,Dursun Irk +2 more
TL;DR: In this paper, the regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method and the same method is applied to the time-split RLW equation.
Journal ArticleDOI
Approximation of the RLW equation by the least square cubic B-spline finite element method
İdris Daǧ,M. Naci Özer +1 more
TL;DR: In this article, the regularized long wave (RLW) equation is solved numerically by giving a new algorithm based on a kind of space-time least square finite element method, in which a combination of cubic B-splines is used as an approximate function.
Journal ArticleDOI
A B-spline finite element method for the regularized long wave equation
TL;DR: In this paper, a Galerkin method with quadratic B-spline finite elements was used to solve the regularized long wave equation numerically and time integration of the resulting system of ordinary differential equations was effected using a Crank-Nicolson approximation.
Journal ArticleDOI
Solving the generalized regularized long wave equation on the basis of a reproducing kernel space
Maryam Mohammadi,Reza Mokhtari +1 more
TL;DR: On the basis of a reproducing kernel space, an iterative algorithm for solving the generalized regularized long wave equation is presented and the approximate solution u"n is constructed by truncating the series to n terms.
References
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Journal ArticleDOI
Model Equations for Long Waves in Nonlinear Dispersive Systems
TL;DR: In this article, the authors studied mathematical models for the unidirectional propagation of long waves in systems that manifest nonlinear and dispersive effects of a particular but common kind.
Book
Quasilinearization and nonlinear boundary-value problems
Richard Bellman,Robert E. Kalaba +1 more
TL;DR: Quasilinearization and nonlinear boundary value problems as discussed by the authors, where the boundary value problem is formulated as a quadratic equation of the value of a boundary value.
Journal ArticleDOI
Calculations of the development of an undular bore
TL;DR: In this paper, the growth of an undular bore from a long wave is described, which forms a gentle transition between a uniform flow and still water, and a physical account of its development is followed by the results of numerical calculations.
Journal ArticleDOI
The Stability of Solitary Waves
TL;DR: In this article, it was shown that the Kortewegde-de-vries equation is invariant with time, and the stability of the solution of this equation is established.
Book
Dynamic Programming and Partial Differential Equations
TL;DR: In this paper, it was shown that dynamic programming applied to the calculus of variations leads to various classes of partial differential equations, and the following chapter we will discuss this further in detail.