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Page 8133 of Mathematical Reviews Vol. , Issue 2004j
[page]
2004
Mathematical Reviews
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8133 65M _ Partial differential equations, initial value and time-dependent initial-boundary value problems
a robust time-discretization of the projection method that guar- antees better stability properties ...
This methodology must be consistent with the basic solution technique for partial differential equations. ...
Page 4878 of Mathematical Reviews Vol. , Issue 95h
[page]
1995
Mathematical Reviews
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Summary: “We consider the wave equation in a moving domain for which approximation by the Galerkin method is an open ques- tion. ...
In the general situation we are concerned with here, that differential system is a third-order one; we show here the convergence of the algorithm for small final time rt.” ...
Generalized Time Integration Schemes for Space-Time Moving Finite Elements
[article]
2013
arXiv
pre-print
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In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. ...
We follow a method of lines approach and utilize an underlying tensor-product finite element space that permits the mesh to evolve continuously in time and undergo discontinuous reconfigurations at discrete ...
For parabolic equations, the method of lines is an efficient approach for computing a numerical solution by converting the partial differential equation into a coupled system of ordinary differential equations ...
arXiv:1310.7611v1
fatcat:r2skgu24tvftnkfysn4xvw4bp4
Bandwidth-based mesh adaptation in multiple dimensions
2018
Journal of Computational Physics
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Spectral methods are becoming increasingly prevalent in solving time-varying partial differential equations due to their fast convergence properties. ...
It is then integrated into a Fourier spectral moving mesh method, using the parabolic Monge-Ampère equation for mesh control. ...
Introduction Spectral methods are increasingly being used for the numerical solution of differential equations [1] . ...
doi:10.1016/j.jcp.2018.06.009
fatcat:dvqg2rrlqbbyzpchbjb4oiynli
A Mesh-Free Collocation Method Based on RBFs for the Numerical Solution of Hunter–Saxton and Gardner Equations
2022
Mathematical Problems in Engineering
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In this paper, the radial basis function (RBF) collocation method is applied to solve nonlinear partial differential equations (PDEs). ...
The stability of the scheme is discussed by the spectral matrix method and validated computationally. ...
Conclusion A mesh-free collocation method based on radial basis functions (RBFs) is applied to approximate time-dependent PDEs. e approximate solutions of the Hunter-Saxton and Gardner equations have been ...
doi:10.1155/2022/2152565
fatcat:s6lw4fwd7ncd7bwqmevouz34yu
A spectral multidomain method for the solution of hyperbolic systems
1986
Applied Numerical Mathematics
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Morcholsne,
"Inhomogeneous
flow calculations
by spectral
methods:
mono-domain
and multl-domaln
techniques,"
in Spectral Methods for Partial
Differential
Equations,
(D. Gottlleb,
M. Y. ...
We have described
a simple
approximation
which
allows
a multidomain
spectral solution of quasilinear
hyperbolic
equations. ...
Final Reoort
Abstract
Submitted to Applied Numerical Mathematics A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations has been developed. ...
doi:10.1016/0168-9274(86)90030-9
fatcat:j3vhv5xinng7fl73d5tvjvlx7y
A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements
2018
Journal of Computational Mathematics
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In this paper, we analyze and provide numerical experiments for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. ...
We follow a method of lines approach and utilize an underlying tensor-product finite element space that permits the mesh to evolve continuously in time and undergo discontinuous reconfigurations at discrete ...
The work of this author was supported by the National Science Foundation under contract DMS-1318480. ...
doi:10.4208/jcm.1805-m2017-0102
fatcat:2orkqbhavnh45gkp2uutamhpa4
Spectral method for time dependent Navier-Stokes equations
2016
Miskolc Mathematical Notes
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The paper is focused on the numerical investigation of the Navier-Stokes equation applying a spectral method. A MATLAB code is developed and used for simulation. ...
The incompressible two-dimensional flow in a square container called lid-driven cavity is tested as a benchmark problem. ...
Applying the SPECTRAL METHOD FOR TIME DEPENDENT NAVIER-STOKES EQUATIONS 47 SIBE semi-discretization method, approximation of the differential equation is @u @t D L.u/ C N.u/; where L is a linear, N is ...
doi:10.18514/mmn.2016.1815
fatcat:24yw4y6k6bf6rbfdvfzhho6ngm
Page 5931 of Mathematical Reviews Vol. , Issue 98I
[page]
1998
Mathematical Reviews
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Methods Partial Differential Equations 13 (1997), no. 6, 673-697. ...
An IMPES method is applied in an adaptive composite grid to track the front of a moving solution An object-oriented programming technique is used. ...
Chebyshev collocation method and multi-domain decomposition for Navier-Stokes equations in complex curved geometries
1993
Journal of Computational Physics
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In our collocation method, the second-order partial differential equation (pde) is satisfied at given points by the approximate solution. ...
The methods for 2D structured grid generation are cast into three groups: methods involving the solution of partial differential equations, conformal mappings, and grids created by interpolation from the ...
doi:10.1016/s0021-9991(83)71105-8
fatcat:zvefywoh25bkdpqfqkfhywq6o4
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
2014
Journal of Computational Physics
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We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical ...
We propose new collocation methods for phase-field models. ...
, efficiency, and simplicity of pseudo-spectral collocation methods. ...
doi:10.1016/j.jcp.2013.12.044
fatcat:rowhptgkqze7ngujgkqeootwfa
Algorithm 690; Chebyshev polynomial software for elliptic-parabolic systems of PDEs
1991
ACM Transactions on Mathematical Software
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Graney of B. P. Research is to be thanked for providing the pool evaporation problem. ...
The essence of the method is to spatially discretize a system of NPDE time-dependent partial differential equations with a spatial mesh of NPTS points and with NV coupled ordinary differential equations ...
INTRODUCTION In recent years there has been considerable interest in the development of general-purpose codes for time-dependent partial differential equations (see the surveys by Machura and Sweet [15 ...
doi:10.1145/108556.108566
fatcat:tmd4hcv525b27dacikfwh23l2i
Fourier--Padé approximations and filtering for spectral simulations of an incompressible Boussinesq convection problem
2007
Mathematics of Computation
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Here, for a given set of the Fourier coefficients from a periodic piecewise analytic function, we define Fourier-Padé-Galerkin and Fourier-Padé collocation methods by expressing the coefficients for the ...
The collocation method is applied as a postprocessing step to the standard pseudospectral simulations for the one-dimensional inviscid Burgers' equation and the twodimensional incompressible inviscid Boussinesq ...
Acknowledgments We thank David Gottlieb for support of this project and for his useful suggestions. The conversation with Jan S. Hesthaven and Laura Lurati has been helpful. ...
doi:10.1090/s0025-5718-07-01831-5
fatcat:a3ldabmford3nlk72pkrh7dfxu
Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method
2011
International Journal for Numerical Methods in Engineering
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Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). ...
Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical ...
In summary, the present meshless formulation is very effective for modeling and simulation of fractional partial differential equations, and it has good potential in development of a robust simulation ...
doi:10.1002/nme.3223
fatcat:vcp5jvcbvnefvf2slhy2tcska4
author index volume
2006
Journal of Computational and Applied Mathematics
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Zafer, Perron's theorem for linear impulsive differential equations with distributed delay 204-218 Alhumaizi, K., A moving collocation method for the solution of the transient convection- Galperin, A., ...
Ozawa, Numerical method of estimating the blow-up time and rate of the solution of ordinary differential equations-An application to the blow-up problems of partial differential equations 614-637 Hongbing ...
doi:10.1016/s0377-0427(06)00279-2
fatcat:wmrtmwomiret3je2zlm44srjxi
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