Solving Single Phase Fluid Flow Instability Equations Using Chebyshev Tau- QZ Polynomial

Stability analysis of stratified two-phase liquid-gas flow in a horizontal pipe

This study aimed at linear stability analysis of the stratified two-phase liquid-gas flow in a horizontal pipe. First, equations governing the linear stability of flow in each phase and boundary conditions were obtained. The governing equations were eigenvalue Orr Sommerfeld equations which are difficult and stiff problems to solve. After obtaining the velocity profiles of the gas and liquid ph...

Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems

The Chebyshev tau method is examined in detail for a variety of eigenvalue problems arising in hydrodynamic stability studies, particularly those of Orr-Sommerfeld type. We concentrate on determining the whole of the top end of the spectrum in parameter ranges beyond those often explored. The method employing a Chebyshev representation of the fourth derivative operator, D 4, is compared with th...

Solving Diophantine equations x 4 + y 4 = qz p

We give a method to solve generalized Fermat equations of type x 4+y4 = qz, for some prime values of q and every prime p bigger than 13. We illustrate the method by proving that there are no solutions for q = 73, 89 and 113. Math. Subject Classification: 11D41,11F11

Solving Polynomial Equations

Solving Monotone Polynomial Equations

We survey some recent results on iterative methods for approximating the least solution of a system of monotone fixed-point polynomial equations.

Fractional Calculus for Solving Abel’s Integral Equations Using Chebyshev Polynomials

Abstract In this paper, the numerical method for solving Abel’s integral equations is presented. This method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply fractional properties for solving Abel’s integral equations of the first and second kind. The fractional operator is considered in the sense of RiemannLiouville. Although Abel’s integral equations as singu...