Finite Differencing: Differentiation and Integration
A number of problems of physics and astronomy appear as Ordinary Differential Equations (ODEs). A practical approach to their solution starts with an approximation to the derivative operator. Broadly, this can be approached by finite differencing or by exact differentiation following a spectral representation. Here, we focus on the first, motivated by an elementary consideration of the problem of estimating velocities and accelerations from particle trajectories. The methods discussed here will be applied to numerical solutions of some illustrative ODEs.
KeywordsAngular Momentum Circular Orbit Cosmological Horizon Spin Angular Momentum Midpoint Rule
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