A modification of pseudo-spectral method for solving a linear ODEs with singularity

On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations

“…Problem 1 was taken from [3] . This problem was solved with Runge-Kutta of different orders and a maximum error of 3.0×10 −1 were recorded.…”

“…The prime denotes that the first term in the expansion is halved. In this method, as against the use of a function V(x) as in the standard Tau method and the Pseudospectral method [2,3,7] , we instead of using the Chebyshev polynomial as a polynomial we exploit the trigonometric property of Chebyshev function.…”

“…In [2] and [3] , the researchers focused on differential equations in which one of the coefficient function or solution function is not analytic on the interval of definition. Weak aspect of spectral methods in solving this kind of problems were studied in [2] and [3] and the researchers came up with modifications to the spectral method which proved to be more efficient when compared with existing ones.…”

“…In this article, we present a variation of the collocation (pseudo-spectral) method to solve the problems of [2] and [3] . The pseudo-pseudo-spectral method (the method introduced in this article) is seen to be efficient and competes favorable with other wellknown standard methods like the Tau method, Galerkin Method and the Pseudo-spectral (collocation) method.…”

Multiple solutions of mixed convection in a porous medium on semi-infinite interval using pseudo-spectral collocation method

“…These polynomials have very good properties in the approximation of functions so that appear frequently in several fields of mathematics, physics and engineering. Spectral collocation methods [4,5] based on Chebyshev polynomials (also is called pseudo-spectral method) have been used to solve numerically differential equations by many authors (see for instance [6][7][8][9][10][11][12]). This method is accomplished successfully by using Chebyshev polynomials approximation and generating approximations for the higherorder derivatives through successive differentiation of the approximate solution.…”