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

Differential mental growth model

The task of optimizing the intellectual potentials of our children and adolescents has required a new urgency that we develop all our human resources to meet the worldwide challenges. From amongst the factors in the cognitive domain that affect learning efficiency, the intelligence is of prime importance. In this paper we are concerned with patterns of intellectual development and have attempted to formulate a differential model, which justifies the mentality of a person at every stage of the age