Physics 410/555: Root Finding & Non Linear Equations
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Last updated January 2007
- 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 (PDF). Lecture version (PDF).
- Part II -- Source code and related: bisect through nlbvp1d
(PDF)
- Lecture 1
- 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.
- Lecture 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 (PDF) for guess_factor = 1.
- Plot of results from convergence test using levels 5, 6
and 7 (PDF) for guess_factor
= 1.
- Plot of three distinct solutions generated with different
values of guess_factor (PDF)
- Detail of above plot (PDF).
- Nlbvp1d:
Script which runs nlbvp1d and generates the above plots.