Quartic C3-spline collocation method for solving second-order initial value problems

This paper introduces and analyzes a new formula for integrating special second-order, periodic and nonperiodic, initial value problems in ordinary differential equations. The presented formula is based on quartic C3-splines as an approximation to the exact solution of the initial value problem, y″(x) = f(x, y), y(0) = y0, y′(0) = y′0. It turns out that the proposed method is a continuous extension of the well-known fourth-order Numerov's method and hence possesses nonvanishing intervals of periodicity and absolute stability.