Pseudospectral method for numerical solution of DAEs with an error estimation

An Opertional Method for The Numerical Solution of Two Dimensional Linear Fredholm Integral Equations With an Error Estimation

A modified pseudospectral method for numerical solution of ordinary differential equations systems

In this paper, numerical solution of first-order systems of ordinary differential equations (ODEs) is considered and an error estimation method is proposed. By this method, the efficiency of pseudospectral method to solve the systems is determined and a modified pseudospectral method is presented. Furthermore, with providing some examples, the aforementioned cases are dealt with numerically. 20...

A modified Chebyshev pseudospectral DD algorithm for the GBH equation

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...

Solving Nonlinear Differential Algebraic Equations by an Implicit GL(n, R) Lie-Group Method

Usually, n is larger than m. When m = 0, the DAEs reduce to the ODEs. There are many numerical methods used to solve ODEs, but only a few is used to solve DAEs [1–5]. A lot of engineering problems are modelled as a combination of ODEs and NAEs, which are abbreviated as differential algebraic equations (DAEs). The DAEs are both numerically and analytically difficult than the ODEs. Recently, ther...

Error Estimation of Pseudospectral Method for Solving the Barotropic Vorticity Equation

The barotropic vorticity equation model is very important in the research of meteorological science and applied mathematics. Many scientists pay attention to the research of numerical methods of this equation. The early works were mainly concerned with finite difference methods [2, 4, 8, 9, 13]. The spectral method has a convergence rate of ”infinite” order, i.e., the error decays faster than a...