A Nonlinear Glerkin Method ' The Two - Level Chebyshev Collocation Case
نویسندگان
چکیده
In this article we study the implementation of the Nonlinear Galerkin method as a multiresolution method when a two-level Chebyshev-collocation discretization is used. A fine grid containing an even number of Gauss-Lobatto points is considered. The grid is decomposed into two coarse grids based on half as many Gauss-Radau points. This splitting suggests a decomposition of the unknowns in low modes and high modes components which is convenient also in the physical space. A nonlinear Galerkin scheme is then applied to a linear parabolic equation in the case of a Chebyshev-Legendre scheme. L2-norm stability is proved.
منابع مشابه
Rational Chebyshev Collocation approach in the solution of the axisymmetric stagnation flow on a circular cylinder
In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...
متن کاملChebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations
We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkinmethod while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and i...
متن کاملA Chebyshev-Gauss-Radau Scheme For Nonlinear Hyperbolic System Of First Order
A numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral collocation method is presented in this article. A Chebyshev-Gauss-Radau collocation (C-GR-C) method in combination with the implicit RungeKutta scheme are employed to obtain highly accurate approximations to the mentioned problem. The collocation points are the Chebyshev interpolation n...
متن کاملMultiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method
The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in so...
متن کاملA Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
We are concerned with linear and nonlinear multi-term fractional differential equations (FDEs). The shifted Chebyshev operationalmatrix (COM) of fractional derivatives is derived and used together with spectral methods for solving FDEs. Our approach was based on the shifted Chebyshev tau and collocation methods. The proposed algorithms are applied to solve two types of FDEs, linear and nonlinea...
متن کامل