Efficient direct solvers based on the Chebyshev-Galerkin methods for second and fourth order equations are presented. They are based on appropriate base functions for the Galerkin formulation which lead to discrete systems with special structured matrices which can be efficiently inverted. Numerical results indicate that the direct solvers presented in this paper are significantly more accurate...

The incomplete elliptic integral of the second kind, EðsinðTÞ;mÞ R T 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m sinðT Þ q dT 0 where m 2 1⁄20;1 is the elliptic modulus, can be inverted with respect to angle T by solving the transcendental equation EðsinðTÞ;mÞ z 1⁄4 0. We show that Newton’s iteration, T 1⁄4 T EðsinðTÞ;mÞ z f g ffiffiffiffiffi...

The purpose of this note is to extend in a simple and unified way some results on orthogonal polynomials with respect the weight function|Tm(x)|p1−x2,−1−1. Namely, provides an explicit representation recurrence coefficients for above function these terms known functions.

In this paper, the two-dimensional second kind Chebyshev wavelets are applied for numerical solution of the time-fractional telegraph equation with Dirichlet boundary conditions. In this way, a new operational matrix of fractional derivative for the second wavelets is derived and then this operational matrix has been employed to obtain the numerical solution of the above mentioned problem. The ...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...