Numerical methods topics:

• Introduction - errors
• Root-finding
• Interpolation
• Numerical integration
• 1st order differential equations
• 2nd order differential equations
• Linear systems
• Finite difference methods
• The Duffing equation
• Approximation of functions
• The numerical evaluation of mathematical functions
• Special inverse functions
• The derivation of Runge-Kutta schemes
• Interpolation for Runge-Kutta schemes

The following Maple worksheets can be downloaded.

They are all compatible with Classic Worksheet Maple 10.

Introduction and free oscillations - duff1.mws

• The double-well oscillator and the Duffing equation
• The Duffing equation for free oscillations
• A periodic solution through both wells

Damped oscillations - duff2.mws

• The Duffing equation for damped oscillations
• A sample numerical solution
• The two basins of attraction in the phase plane
• Solutions attracted to each well

Forced and damped oscillations - duff3.mws

• The Duffing equation with both damping and forcing terms
• A non-chaotic solution
• The transition to chaos

Forced and damped oscillations (continued) - duff4.mws

• A periodic solution with period 4 times the period of the driving force
• Reconstructing the solution and its symmetrical counterpart
• Poincare sections

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