Chapter 9

Solving Ordinary Differential Equations

Note: While inclusion of all components in this chapter would, in principle, be possible, selection of only a few of MACSYMA, MAPLE, Mathematica, IDL, MATLAB, FORTRAN (with or without Numerical Recipes), and C (with or without Numerical Recipes) would probably be more common.

9.1Sample Problems
9.1.1 Projectile in a Viscous Medium
9.1.2 Radioactive Decay
9.1.3 Exponential and Logistic Growth
9.1.4 Forced, Driven, Damped Harmonic Oscillation
9.1.5 An LRC Resonant Circuit
9.1.6 Coupled Oscillators
9.1.7 Motion under Central Forces
9.1.8 Standing Waves in a String
9.1.9 The Schrodinger Equation in One Dimension
9.2Laplace Transforms
9.3Solving ODEs Symbolically with Macsyma
9.3.1 Projectile in a Viscous Medium
9.3.2 Logistic Growth
9.3.3 Damped Harmonic Oscillator
9.3.4 Chain Radioactive Decay
9.3.5 Coupled Oscillators
9.3.6 Standing Waves in a String
9.3.7 Infinite Depth Quantum Well
9.3.8 Finding Solutions by Series Methods
9.4Solving ODEs Symbolically with Maple
9.4.1 Projectile in a Viscous Medium
9.4.2 Logistic Growth
9.4.3 Damped Harmonic Oscillator
9.4.4 Chain Radioactive Decay
9.4.5 Coupled Oscillators
9.4.6 Standing Waves in a String
9.4.7 Infinite Depth Quantum Well
9.4.8 Finding Solutions by Series Methods
9.5Solving ODEs Symbolically with Mathematica
9.5.1 Projectile in a Viscous Medium
9.5.2 Logistic Growth
9.5.3 Damped Harmonic Oscillator
9.5.4 Chain Radioactive Decay
9.5.5 Coupled Oscillators
9.5.6 Standing Waves in a String
9.5.7 Infinite Depth Quantum Well
9.5.8 Finding Solutions by Series Methods
9.6Algorithms for Solving ODEs Numerically
9.6.1 Euler's Method
9.6.2 Improved Euler Method
9.6.3 Runge-Kutta Methods
9.6.4 Assessing Accuracy
9.6.5 Adaptive Methods
9.6.6 Multistep Methods
9.7Solving ODEs Numerically with IDL
9.7.1 Using Elementary Commands
9.7.2 Defining ODEs for IDL
9.7.3 The Procedures rk4, lsode, ludiffeq_23, and ludiffeq_45
9.7.4 Chain Radioactive Decay
9.7.5 Damped Harmonic Oscillator
9.7.6 Planetary Orbits
9.7.7 Standing Waves in a String
9.7.8 The Quantum Harmonic Oscillator
9.7.9 Pro-files in the Public Library
9.8Solving ODEs Numerically with MATLAB
9.8.1 Using Elementary Commands
9.8.2 Defining ODEs for MATLAB
9.8.3 The Procedures ode23, ode45, and ode113
9.8.4 Chain Radioactive Decay
9.8.5 Damped Harmonic Oscillator
9.8.6 Planetary Orbits
9.8.7 Standing Waves in a String
9.8.8 The Quantum Harmonic Oscillator
9.8.9 M-files in the Public Library
9.9Solving ODEs Numerically with Macsyma
9.10Solving ODEs Numerically with Maple
9.11Solving ODEs Numerically with Mathematica
9.12Solving ODEs Numerically with FORTRAN
9.12.1 FORTRAN Programs from Scratch
9.12.2 Using Numerical Recipes
9.13Solving ODEs Numerically with C
9.13.1 C Programs from Scratch
9.13.2 Using Numerical Recipes
9.14.1 ... using Symbolic Methods
9.14.2 ... using Numerical Methods
9.14.3 ... using Numerical Recipes
9.AListing of decay.f
9.BListing of decayrk4.f
9.CListing of decayrkqs.f
9.DListing of decay.c
9.EListing of decayrk4.c
9.FListing of decayrkqs.c

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