Some similarity solutions of inviscid compressible fluid flow equations

Employing one parameter group of transformation some new exact solutions of the equations governing the steady inviscid compressible fluid are determined. Some of the solutions involve arbitrary function enabling us to construct a large number of solutions of the flow equations. The streamline patterns of some of the solutions in unbounded and bounded regions are also presented

new variable step size algorthm for solving initial value problems

Polynomials constructed by usual interpolation methods are less accurate as compared to the tools due to Chebyshev. Hence the use of Chebychev's nodes to produce the solution of initial value problems promises more accurate results. In this work a new algorithm is developed using nodes generated by Chebychev's method that are used as points where solution are produced for a number of Linear and Non-Linear Initial Value Problems using classical Runge-Kutta method. The improvement in accuracy is found even when the number of nodes is small, that makes this algorithm better than other valuable step-size methods