(71B) Euler-Taylor method for the HP-71B

[Namir]

Albert,

For last last month I have been studying numerical methods for ODE that are based on Runge-Kutta methods. There is a VAST number of variants of the RK methods! I happen to browse at early pages of a book by Leon Lapidus and I noticed the Tayler expansion. At that moment, something registered in my brain and I decided to extend the basic Euler method to include the second derivative. The increase in accuracy relative to the CPU effort is very good when you compare it with different variants of the Runge-Kutta methods that calculate k1 through k5 or k6 intermediate values per iteration. I realized that extending the Euler method is very suitable for our beloved calculator. Your contibution to approximate the second derivative is key in making the method more practical to use.

Namir