Euler-Taylor method - Printable Version +- HP Forums ( https://www.hpmuseum.org/forum)+-- Forum: HP Calculators (and very old HP Computers) ( /forum-3.html)+--- Forum: General Forum ( /forum-4.html)+--- Thread: Euler-Taylor method ( /thread-14124.html) |

Euler-Taylor method - Namir - 12-07-2019 04:40 PM
I posted new listings for the HP-41C and HP-71B (two versions) that implement an extended version of Euler's method for solving ODEs. The new method uses the Taylor expansion and include the first and second derivatives. The aim of the ODE solver is to integrate the first derivative. Including the second derivative allows the new method to give better accuracy at less CPU effort. To integrate f'(x,y) from x=a to x=b, give y(a), we use an extended version of the Euler method that includes the first AND second derivatives. Since we know f'(x,y) we can derive f''(x,y) and use the following formula: y = y + h*f'(x,y) + h^2/2*f''(x,y) The method works especially if it is easier to derive the seond derivative from the first one AND if integrating the first derivating is very difficult. Check the listings or the HP-41C and HP-71B and enjoy! Namir |