Journal ArticleDOI
On the numerical solution of nonlinear Burgers’-type equations using meshless method of lines
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TLDR
A meshless method of lines (MMOL) is proposed for the numerical solution of nonlinear Burgers’-type equations that does not require a mesh in the problem domain, and only a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions.About:
This article is published in Applied Mathematics and Computation.The article was published on 2012-02-05. It has received 36 citations till now. The article focuses on the topics: Regularized meshless method & Singular boundary method.read more
Citations
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Journal ArticleDOI
On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method
TL;DR: In this paper, the authors extended the proposed algorithm for selecting a good value of shape parameter c in solving time-dependent partial differential equations, which is directly connected to the accuracy of the method.
Journal ArticleDOI
Numerical solutions of generalized Burgers–Fisher and generalized Burgers–Huxley equations using collocation of cubic B-splines
R. C. Mittal,Amit Tripathi +1 more
TL;DR: A numerical scheme to obtain approximate solutions of generalized Burgers–Fisher and Burgers-Huxley equations and it is shown that the method is unconditionally stable and the approximate solutions have been computed without using any transformation or linearization.
Journal ArticleDOI
Efficient numerical techniques for Burgers' equation
Vijitha Mukundan,Ashish Awasthi +1 more
TL;DR: New efficient numerical techniques for solving one dimensional quasi-linear Burgers' equation used in the study of turbulence, boundary layer behavior, shock waves, convection dominated diffusion phenomena, gas dynamics, acoustic attenuation in fog and continuum traffic simulation are presented.
Journal ArticleDOI
Unconditionally stable meshless integration of time-domain Maxwell's curl equations
TL;DR: A formulation of the alternating direction implicit scheme is proposed into the meshless framework, not constrained by a grid in space and unconditionally stable in time, and is validated by numerical simulations.
Journal ArticleDOI
A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers' equation
Yan Guo,YuFeng Shi,Yi-min Li +2 more
TL;DR: A high-order finite volume compact scheme is proposed to solve one dimensional Burgers' equation and the essentially non-oscillatory and high resolution results are shown to be more accurate than some numerical results given in the literature.
References
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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.
Journal ArticleDOI
Multiquadrics--a scattered data approximation scheme with applications to computational fluid-dynamics-- ii solutions to parabolic, hyperbolic and elliptic partial differential equations
TL;DR: In this paper, the authors used MQ as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation, and showed that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.
Approximation scheme with applications to computational fluid-dynamics-- i surface approximations and partial derivative estimates
TL;DR: In this article, the authors presented an enhanced multiquadrics (MQ) scheme for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.
Journal ArticleDOI
Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates
TL;DR: In this article, the authors presented a powerful, enhanced multiquadrics (MQ) scheme developed for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.
Book
The Numerical Method of Lines: Integration of Partial Differential Equations
TL;DR: The Laplacian Operator in Various Coordinate Systems and some Applications of the Numerical Method of Lines are described, as well as some applications of the ODE and ODE/PDE Applications.