Numerical Integration

• Features and Experience:
  • Trapezoidal and Simpson's Rules
  • Data management in realistic computational environments
  • Multi-Language computation (C++, C, and FORTRAN)
  • Note: It will be a good project for juniors
• Source code & Documentation: Numer_Integration.CF.tar, Numer_Integration.TEX.tar (LaTeX source), and Numer_Integration.ps.

ODE Solvers

• Features:
  • Euler, Heun, and RK4 methods
  • They compute vector solutions of general dimensions.
  • Language: C++, C, and F77
• Source code & Documentation: ODESOL.CF.tar, ODESOL.TEX.tar, and ODESOL.ps
• Note: The code is organized from projects assigned to MA214, MA/CS321, and MA/CS537.

Standard Schemes for One-Way Waves

• Features:
  • Equation: Ut+aUx=0
  • Domain: a line segment
  • Mesh: Uniform or non-uniform
  • Discretizer: Various temopral and spatial schemes
  • Time-stepping procedure: The theta-method
  • Language: C++, C, and F77
  • Note: This can be a good project for beginning graduates
• Source code & Documentation: OneWayWave.CF.tar and OneWayWave.jpg.
• Suggested classroom applications:
  • Extend it for modern schemes, such as ENO, MUSCL, and QUICK.
  • Apply it for the heat equations in 1D and 2D.

Curve Fitting (Regression Analysis)

• Features:
  • Problem: Curve fitting with nonlinear trial functions
  • Algorithm: Alternating fractional fitting
  • Language: C++, C, and F77
  • Note: It is suitable for graduate students
• Source code & Documentation: Curve_Fitting.CC.tar and Curve_Fitting.pdf.
• Suggested classroom applications:
  • Let students adjust the code for various different fitting functions and data.