Simulations in Waves and Optics The Consortium for Upper Level Physics Software The CUPS software and associated text materials are copyrighted. You have permission to reproduce the text material for use in your courses during beta testing. Please do not give the programs or text materials to colleagues, since we would like to keep track of it.

Wolfgang Christian
Andrew Antonelli
Susan Fischer
Department of Physics, Davidson College,
Davidson, North Carolina 28036, U.S.A

Robin A. Giles
Department of Physics and Astronomy, Brandon University,
Brandon, Manitoba R7A 6A9, Canada

Brian W. James
Department of Physics, University of Salford,
Salford, M5 4WT, United Kingdom

Ronald Stoner
Department of Physics, Bowling Green University,
Bowling Green, OH 43403

• Contents
• List of Tables
• List of Figures
• The Wave Equation and Other PDEs
  • Introduction
  • Classification of Partial Differential Equations
  • Physics of Partial Differential Equations
    • Classical Wave Equation
    • Klein-Gordon and Schrödinger Equations
    • Nonlinear Klein-Gordon Equations
    • Diffusion Equation
  • Numerical Methods
    • Finite Difference Approximation
    • Klein-Gordon Equation; Numerical Method
    • Classical Wave Equation; Numerical Method
    • Schrödinger Equation; Numerical Method
    • Diffusion Equation; Numerical Method
    • Boundary Conditions
      • Fixed Boundary
      • Periodic Boundary
      • Absorbing Boundary
  • Running WAVE
    • A Quick Tour of Wave
    • Controlling Execution Speed
    • Inspector panels/Mouse-Accessible Objects
    • Menu Items
    • Hot Keys
  • Exercises
    • Visualization and Analysis Tools
    • Eigenfunctions
    • Fourier Analysis
    • Green's Functions and Propagators
    • Superposition and Interference
    • Resonance
    • Steps and Barriers
    • Multilayer Films
    • Resonators
    • WKB Approximation
    • Nonlinear Klein-Gordon Equations
    • Numerical Effects
    • Program Modification
  • Acknowledgements
• References
• Index
• About this document ...