Numerical solutions of the Burgers' equation by the least-squares quadratic B-spline finite element method
TLDR
In this paper, a least-squares quadratic B-spline finite element method for calculating the numerical solutions of the one-dimensional Burgers-like equations with appropriate boundary and initial conditions is presented.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2004-05-01 and is currently open access. It has received 200 citations till now. The article focuses on the topics: Mixed finite element method & Boundary knot method.read more
Citations
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Journal ArticleDOI
Numerical solutions of nonlinear Burgers’ equation with modified cubic B-splines collocation method
R. C. Mittal,R.K. Jain +1 more
TL;DR: The numerical approximate solutions to the Burgers’ equation have been computed without transforming the equation and without using the linearization.
Journal ArticleDOI
A Haar wavelet quasilinearization approach for numerical simulation of Burgers’ equation
TL;DR: An efficient numerical scheme based on uniform Haar wavelets and the quasilinearization process is proposed for the numerical simulation of time dependent nonlinear Burgers' equation and is found to be accurate, simple, fast, flexible, convenient and has small computation costs.
Journal ArticleDOI
A hybrid numerical scheme for the numerical solution of the Burgers’ equation
TL;DR: A hybrid numerical scheme based on Euler implicit method, quasilinearization and uniform Haar wavelets has been developed for the numerical solutions of Burgers’ equation and is found to be accurate, simple, fast, flexible, convenient and at small computation costs.
Journal ArticleDOI
Fourth-order finite difference method for solving Burgers’ equation
TL;DR: Fourth-order finite difference method for solving nonlinear one-dimensional Burgers’ equation is presented and an upper bound for the error is derived.
Journal ArticleDOI
Numerical solution of Burgers' equation with modified cubic B-spline differential quadrature method
Geeta Arora,Brajesh Kumar Singh +1 more
TL;DR: The presented method is seen to be easy, powerful, efficient and economical to implement as compared to the existing techniques for finding the numerical solutions for various kinds of linear/nonlinear physical models.
References
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Book
Numerical solution of partial differential equations : finite difference methods
TL;DR: In this article, the standard finite difference methods of parabolic, hyperbolic, and elliptic equations are discussed, together with the concomitant theoretical work on consistency, stability, and convergence.
Book ChapterDOI
A mathematical model illustrating the theory of turbulence
TL;DR: In this article, the application of statistical analysis and statistical mechanics to the problem of turbulent fluid motion has attracted much attention in recent years, and the authors investigated a complicated system of nonlinear equations, in order to find out enough about the properties of the solutions of these equations that insight can be obtained into the various patterns exhibited by the field and that data can be derived concerning the relative frequencies of these patterns in the hope that in this way a basis may be found for the calculation of important values.
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On a quasi-linear parabolic equation occurring in aerodynamics
TL;DR: In this paper, the Navier-Stokes equations for one-dimensional non-stationary flow of a compressible viscous fluid are compared to the shock wave theory of a model of turbulence.