[PDF] Top 20 A Crank–Nicolson collocation spectral method for the two dimensional telegraph equations

... graph equations has significant meaning. However, the telegraph equations in the real- world problems usually include the complex known data, such as the complicated initial and boundary value ... See full document

... Schrödinger equations were discussed in [, ], and for recent schemes for solving PDEs see ...Gauss-Radau collocation (SJ-GR-C) methods in two consec- utive stages for providing a high accurate ... See full document

... one-space dimensional linear hyperbolic equa- ...Tau method. The authors of [22] used Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph ...order two-space- ... See full document

... difference method for solving 2-dimensional diffusion equation is ...The method employs Crank-Nicolson scheme to improve fi- nite difference formulation and its convergence and sta- ... See full document

... mans method as a simplified model to interpret the theory of turbulence ...one- dimensional form of this equation, Cole [20] and Hopf [21] found that it can represent the typi- cal features of the shock ... See full document

... classical collocation spectral (CS) method of two-dimensional (2D) Sobolev ...extrapolating collocation spectral (ROECS) method for 2D Sobolev equations so ... See full document

... applied collocation technique with Gauss-Lobatto nodes whereas Xie et ...tau method to determine expansion ...spaced collocation points but expressed the trial solution in terms of Hermite ... See full document

... model equations used to test the accuracy of new numerical methods or computational algorithms ...The two dimensional non-linear Burgers equations are a special form of in compressible ... See full document

... a spectral collocation method based on integrated Chebyshev polyno- mials for numerically solving biharmonic boundary-value ...governing equations are also forced to be satisfied exactly at the ... See full document

... element method (FEM), finite volume element method (FVEM), and spectral method are considered to be four well-known nu- merical ...the spectral method can attain higher accuracy ... See full document

... the two-dimensional (2D) Sobolev ...semi-discrete Crank-Nicolson (CN) formulation with second-order accuracy about time for the 2D Sobolev ... See full document

... Stokes equations about vorticity–stream functions has not only the second-order accuracy in time, but also is formed by system of two relatively independent linear equations for vorticity–stream ... See full document

... the Crank-Nicolson method directly to the Burgers’ equation, ...present method is compared to the absolute error of the two existing methods for two test ...The method is ... See full document

... phenomena, spectral methods have emerged as a very powerful and ef- ficient numerical technique, which are a well-known class of numerical methods for the solutions of various differential equations due to ... See full document

... In this work we will approximate the solution of 1.1 using a discontinuous sym- metric Galerkin method with interior penalties for the spatial discretization and extrapolated Crank-Nicolson ... See full document

... by two numerical techniques, that is, the Monte-Carlo simulation and the Crank-Nicolson finite difference ...simulation method, the concept of a random walk is used in the simulation of the ... See full document

... ference method and the series method (mainly Adomian decomposition and variational iterative ...difference method has a wide application ...difference method are reflected in solving problems in ... See full document

... (RBFs) method has become known as a powerful tool for the scattered data interpolation prob- ...Kansa’s method developed by Kansa in 1990 [20, 21], is obtained by directly collocating RBFs, particularly the ... See full document

... The Crank-Nicolson (CN) scheme solves the discretized Maxwell’s equations by a full time-step size with one marching procedure and takes the average of a forward difference and a backward difference in ... See full document

... The present paper describes instability (fingering) phenomenon in double phase flow of two immiscible fluids (water and oil) through homogeneous porous medium. The displacement of native oil by another of lesser ... See full document