Physics 410: Root Finding & Non Linear Equations

• Source code covered in class can be found on the phys410 account on the lnx machines in ~phys410/nonlin/...
• General References
  • Numerical Recipes (Chapter 9)
    • Section 9.1 Introduction (PDF).
    • Section 9.2 Bracketing and Bisection (PDF).
    • Section 9.4 Newton-Raphson Method Using Derivative (PDF).
    • Section 9.6 Newton-Raphson Method for Nonlinear Systems of Equations (PDF).
• Handouts:
  • Part I -- Notes: Solution of Nonlinear Equations (PS). Lecture version (PS).
  • Part II -- Source code and related: bisect through nlbvp1d (PS)
• Lecture 1 (November 30)
  • bisect: Location of bracketed root using bisection.
    • bisect.f: Bisection routine.
    • tbisect.f: Test driver for bisect
    • comf.inc: Include file which defines a common block for global communication with the user-supplied routine (function whose root is sought).
    • Makefile
    • Sample output on lnx1.
  • newtsqrt: Computation of square roots using Newton's method.
    • newtsqrt.f: Program.
    • Makefile
    • Sample output on lnx1.
• Lecture 2 (November 30 & December 2)
  • newt2: Computation of solutions of simple set of non-linear equations (d=2).
    • newt2.f: Program.
    • Makefile
    • Sample output on lnx1.
    • Check of the computation using Maple's numerical root finding capabilities (fsolve).
  • nlbvp1d: Solution of non-linear boundary value problem via finite differencing and mulit-dimensional Newton's method.
    • nlbvp1d.f: Program.
    • Makefile
    • Plot of computed level-6 and exact solutions (PS) for guess_factor = 1.
    • Plot of results from convergence test using levels 5, 6 and 7 (PS) for guess_factor = 1.
    • Plot of three distinct solutions generated with different values of guess_factor (PS)
    • Detail of above plot (PS).
    • Nlbvp1d: Script which runs nlbvp1d and generates the above plots.