Today’s download starts with some simple linear interpolation methods used to solve polynomial equations, leading on to more sophisticated methods using quadratic or inverse quadratic interpolation. Also included is a solver for differential equations using the Cash-Karp Method, which is a refinement of the Runge-Kutta Method.

The current download files are:

Newton’s method:
http://interactiveds.com.au/software/Newtons%20Method.zip
Quadratic and Inverse Quadratic interpolation:
http://interactiveds.com.au/software/ItSolve%20Functions.xls
Brent’s Method
http://www.interactiveds.com.au/software/ItSolve.zip
Ordinary differential equation solver (Cash-Karp Method)
http://interactiveds.com.au/software/ODESolver.zip

More details are given in the following posts:

Approximate Solutions of Polynomial Equations
Function roots with the Inverse Quadratic Method
The Inverse Quadratic Method – 2
The Inverse Quadratic Method 3 – Brent’s Method
Using the AlgLib ODE (Runge-Kutta) Solver with Excel

Basis of the Newton-Raphson Method

Inverse Quadratic Method

Muller’s Method and Brent’s Method functions

Damped Vibration System differential equations

Damped vibration system solution

Buckling load of a column using ODE solver function