Muhammad Younis | Searcharxiv

arXiv2013

Soliton Solutions of Fractional order KdV-Burger's Equation

In this article, the new exact travelling wave solutions of the time-and space-fractional KdV-Burgers equation has been found. For this the fractional complex transformation have been implemented to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations, in the sense of the Jumarie's modified Riemann-Liouville derivative. Afterwards, the improved (G'/G)-expansion method can be implemented to celebrate the soliton solutions of KdV-Burger's equation of fractional order.

math-ph↗

arXiv2013

Non-stationary subdivision schemes originated from uniform trigonometric B-spline

The paper proposes, an algorithm to produce novel m-point (for any integer m>=2) binary non-stationary subdivision scheme. It has been developed using uniform trigonometric B-spline basis functions and smoothness is being analyzed using the theory of asymptotically equivalence. The results show that the most of well-known binary approximating schemes can be considered as the non-stationary counterpart of the proposed algorithm. Furthermore, the schemes developed by the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines as well. Some examples are considered, by choosing an appropriate tension parameter 0<alpha<pi/3, to show the usefulness.

math.NA↗