Abstract
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 C 3-splines as an approximation to the exact solution of the initial value problem, y″( x) = f( x, y), y(0) = y 0, 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.
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