Non-Stiff Equations         Cash-Karp Method

The Cash-Karp formula is a 5(4) Runge-Kutta formula for solving non-stiff systems of initial value ordinary differential equations. It is fully described in the book

 

Numerical Recipes in C (and also Numerical Recipes in Fortran): The Art of Scientific Computing (second edition)

by Press, Flannery, Teukolsky and Vetterling.

 

It is also described in

 

A variable order Runge-Kutta method for initial value problems with rapidly varying right hand sides

J.R. Cash and A.H. Karp, ACM Transactions on Mathematical Software, Vol 16, No.3, Pages 201-222

 

 

The MATLAB code can be found in

 

Numerical Methods in Engineering with Matlab

Jaan Kiusalaas, CUP, August 2005, pages 280-285

 

Programs which implement this method can be found in the ODE section of the above Numerical Recipes books.

 

Then starting from  compute and define

 

A solution at an off step point  can be computed at virtually zero extra cost using

 

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