Exponentially Fitted Chebyshev Based Algorithm as Second Order Initial Value Solver

In this research work, we focus on development of a numerical algorithm which is well suited as integrator of initial value problems of order two. Exponential function is fitted into the Chebyshev polynomials for the formulation of this new numerical integrator. The efficiency, ingenuity and computational reliability of any numerical integrator are determined by investigating the zero stability, consistency and convergence of the integrator. Findings reveal that this algorithm is convergent. On comparison, the solutions obtained through the algorithm compare favourably well with the analytical solutions.