On the derivation, convergence, consistence and stability of a new numerical integrator

For any numerical integrator to be efficient, ingenious and computationally reliable, it is expected that it be convergent, consistent and stable. In this paper, we develop a new numerical integrator which is particularly well suited for solving initial value problems in ordinary differential equations. The algorithm developed is based on a local representation of the theoretical solution to the initial value problem by a nonlinear interpolating function (comprising of the combination of polynomial, exponential and cyclometric functions). We further test whether or not the integrator satisfies the conditions for convergence, consistence and stability. From the analysis presented, it is obvious that the new numerical integrator can provide accurate solution to the original differential equation.