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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. ...
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.” ...
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
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  . ...doi:10.1016/j.jcp.2018.06.009 fatcat:dvqg2rrlqbbyzpchbjb4oiynli
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
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
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
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
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. ...
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
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
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
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
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
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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