Physics 410: Root Finding & Non Linear Equations

• Source code covered in class can be found on the phys410 account on sgi1 in ~phys410/nonlin/ex[123] (organized by lecture).
• General References
  • Numerical Recipes (Chapter 9)
    • Section 9.1 Introduction (PS).
    • Section 9.2 Bracketing and Bisection (PS).
    • Section 9.4 Newton-Raphson Method Using Derivative (PS).
    • Section 9.6 Newton-Raphson Method for Nonlinear Systems of Equations (PS).
• Combined handouts (PS) and slides (PS) for the following lectures.
• Lecture 1 (Nov 9)
  • Handout (PS) and slides (PS).
  • bisect.f: Fortran routine for locating bracketed root using bisection.
    Test driver tbisect.f and include file comf.inc which defines a common block for global communication with the user-supplied routine (function whose root is sought).
    Makefile and sample output on sgi1.
• Lecture 2 (Nov 14)
  • Handout (PS) and slides (PS).
  • newtsqrt.f: Fortran program for computing square roots (solving x^2 - a = 0) using Newton's method.
    Makefile and sample output on sgi1.
• Lecture 3 (Nov 16)
  • Handout (PS) and slides (PS).
  • newt2.f: Fortran program for computing root of simple set of non-linear equations (d=2) discussed in class.
    Makefile and sample output on sgi1 and a check on the computation using Maple's numerical root finding capabilities (fsolve).