new variable step size algorthm for solving initial value problems

ABSTRACT

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: