John D. Cook • 12/23/2025

Bowie integrator and the nonlinear pendulum

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This technical article investigates Bowie's numerical method for solving second-order ODEs (y″ = f(y)), a technique referenced in a 1963 NASA handbook but largely unknown academically. It details applying the method to the nonlinear pendulum equation (y″ = − sin(y)), providing Python implementation, discussing period calculations using elliptic integrals, and comparing nonlinear and linearized solutions.

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#Python #Numerical Methods #Ordinary Differential Equations
Bowie integrator and the nonlinear pendulum

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