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.
| 9.1 | Sample 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 | |
| 9.2 | Laplace Transforms |
| 9.3 | Solving 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 | |
| 9.4 | Solving 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 | |
| 9.5 | Solving 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 | |
| 9.6 | Algorithms 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 | |
| 9.7 | Solving 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 | |
| 9.8 | Solving 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 | |
| 9.9 | Solving ODEs Numerically with Macsyma |
| 9.10 | Solving ODEs Numerically with Maple |
| 9.11 | Solving ODEs Numerically with Mathematica |
| 9.12 | Solving ODEs Numerically with FORTRAN |
| 9.12.1 FORTRAN Programs from Scratch | |
| 9.12.2 Using Numerical Recipes | |
| 9.13 | Solving ODEs Numerically with C |
| 9.13.1 C Programs from Scratch | |
| 9.13.2 Using Numerical Recipes | |
| 9.14 | Exercises |
| 9.14.1 ... using Symbolic Methods | |
| 9.14.2 ... using Numerical Methods | |
| 9.14.3 ... using Numerical Recipes | |
| 9.A | Listing of decay.f |
| 9.B | Listing of decayrk4.f |
| 9.C | Listing of decayrkqs.f |
| 9.D | Listing of decay.c |
| 9.E | Listing of decayrk4.c |
| 9.F | Listing of decayrkqs.c |