Open AccessJournal Article
Approximation of the KdVB equation by the quintic B-spline differential quadrature method
TLDR
In this paper, the Korteweg-de Vries-Burgers (KdVB) equation is solved numerically by anew differential quadrature method based on quintic B-spline functions.Abstract:
In this paper, the Korteweg-de Vries-Burgers’ (KdVB) equation is solved numerically by anew differential quadrature method based on quintic B-spline functions. The weightingcoefficients are obtained by semi-explicit algorithm including an algebraic system with fivebandcoefficient matrix. The L2 and L∞ error norms and lowest three invariants 1 2 I , I and3 I have computed to compare with some earlier studies. Stability analysis of the method isalso given. The obtained numerical results show that the present method performs better thanthe most of the methods available in the literature.read more
Citations
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An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method
TL;DR: In this article, an effective differential quadrature method (DQM) based on modified cubic B-spline (MCB) has been implemented to obtain the numerical solutions for the nonlinear Schrodinger (NLS) equation.
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Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method
R. C. Mittal,Rajni Rohila +1 more
TL;DR: In this article, a modified cubic B-spline based differential quadrature method was used to get numerical solutions of one dimensional reaction-diffusion systems such as linear reactiondiffusion system, Brusselator system, Isothermal system and Gray-Scott system.
Journal ArticleDOI
An Efficient Approximation to Numerical Solutions for the Kawahara Equation Via Modified Cubic B-Spline Differential Quadrature Method
TL;DR: In this paper, the numerical solutions for the Kawahara equation via the Crank-Nicolson-Differential Quadrature Method based on modified cubic B-splines (MCBC-DQM) were obtained.
Journal ArticleDOI
A novel approach for numerical computation of Burgers’ equation in (1 + 1) and (2 + 1) dimensions
Brajesh Kumar Singh,Pramod Kumar +1 more
TL;DR: In this article, a modified extended cubic B-spline differential quadrature (mECDQ) method for time dependent partial differential equations is proposed. But the mECDQ method is not suitable for the case of time dependent PDEs.
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An effective application of differential quadrature method based on modified cubic B-splines to numerical solutions of the KdV equation
TL;DR: In this paper, numerical solutions of the third-order nonlinear Korteweg-de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines.
References
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Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations
TL;DR: In this article, the authors present a direct technique which can be applied in a large number of cases to circumvent the difficulties of programming complex algorithms for the computer, as well as excessive use of storage and computer time.
Journal ArticleDOI
Application of generalized differential quadrature to solve two-dimensional incompressible navier-stokes equations
Chang Shu,Bryan E. Richards +1 more
TL;DR: In this paper, a global method of generalised differential quadrature is applied to solve the two-dimensional incompressible Navier-Stokes equations in the vorticity-stream-function formulation.
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Korteweg‐de Vries Equation and Generalizations. III. Derivation of the Korteweg‐de Vries Equation and Burgers Equation
C. H. Su,C. S. Gardner +1 more
TL;DR: In this paper, the Burgers equation and Kortewegde Vries equation are derived for a wide class of nonlinear Galilean invariant systems under the weak nonlinearity and long-wavelength approximations.
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New insights in solving distributed system equations by the quadrature method—I. Analysis
J.R. Quan,Chuei-Tin Chang +1 more
TL;DR: In this article, the authors derived explicit formulae of the quadrature coefficients for arbitrarily-distributed nodes and for nodes located at the zeros of an orthogonal polynomial.
Journal ArticleDOI
A non-linear equation incorporating damping and dispersion
TL;DR: The steady state solution of the non-linear equation with both damping and dispersion is examined in the phase plane in this paper, where an averaging technique is used to obtain an oscillatory asymptotic solution.