Maple worksheets on numerical root-finding |

Numerical methods topics:

- Introduction - errors
- Root-finding
- Interpolation
- Numerical integration
- 1st order differential equations
- 2nd order differential equations
- Linear systems
- Finite difference methods
- The Duffing equation
- Approximation of functions
- The numerical evaluation of mathematical functions
- Special inverse functions
- The derivation of Runge-Kutta schemes
- Interpolation for Runge-Kutta schemes

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

The bisection method-bisect.mws

- A introduction to root-finding using graphs in conjunction with Maple's
fsolveprocedure.- A procedure for finding a zero of a function by the bisection method:
bisect.

Newton's method-newton.mws

- Explanation of Newton's method.
- A procedure for graphing successive steps of Newton's method:
newton_step- A procedure for finding a zero of a function by Newton's method:
newton.

The secant method-secant.mws

- Explanation of the secant method for root finding.
- A procedure for graphing successive steps of the secant method:
secant_step- A procedure for finding a zero of a function by the secant method:
secant.

Halley'smethod-halley.mws

- The iterative formula for Halley's method.
- Osculating hyperbolas and the Halley iteration formula.
- A procedure for graphing successive steps of the secant method:
halley_step- A procedure implementing Halley's method for root-finding:
halley

The improved "leap-frog" Newtonmethod for root-finding-LFnewton.mws

- The iterative formula for the improved "leap-frog" Newton method.
- A procedure for graphing successive steps of the improved "leap-frog" Newton method:
impnewton_step- A procedure for finding a zero of a function by the improved "leap-frog" Newton method:
impnewton.

Brent's method for root-finding-brent.mws

- Inverse quadratic interpolation and Brent's method.
- A procedure for finding a zero of a function by Brent's method:
brent.

General fixed point iteration for root-finding-itersolve.mws

- Hero's formula for calculating square roots
- Iterative formulas for solving equations
- A procedure for finding a fixed point of a real function:
fixedpoint.- Graphical illustration of iterative solutions
- Oscillating values from an iterative formula

A procedure for finding all roots in an interval where a sign change occurs-allbisect.mws

- A procedure for finding all zeros of a function in an interval where a sign change occurs:
allbisect.

A bisection method is first used to pin down each root to a small interval.

A procedure for finding all roots in an interval-allroots.mws

- A procedure for finding all the zeros of a function in an interval:
allroots.

It is a modification of the procedure allsolve written by Robert Israel from U.B.C.

It makes use of range arithmetic via Maple'sevalr.

Numerical determination of a local maximum or minimum-maxmin.mws

- Golden section search for a maximum or minimum.
- Pictorial example of golden section search.
- Procedures which search for a local maximum or minimum:
goldmax/goldmin.- Searching for a maximum or minimum using parabolic interpolation.
- Pictorial example using parabolic interpolation.
- Procedures which search for a local maximum or minimum:
findmax/findmin.

The logistic family of functions and chaos-chaos.mws

- The logistic family of functions.
- Iterating members of the logistic family.
- Bifurcation
- A procedure for displaying the bifurcation diagram of the logistic family:
logisticdisplay.- The bifurcation diagram of the logistic family.
- Chaos and islands of regularity.
- Finding a parameter value for the 3-cycle.
- Finding a parameter value for the 1st 5-cycle.
- Finding parameter values for the other two 5-cycles.

Root-finding procedures-roots.zip