- #1

maistral

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*I was trying to code a Bogacki-Shampine method for systems of 4 differential equations in my graphing calculator but apparently I lack the sufficient variables needed for it. I tried lowering the orders, ending up in an adaptive Euler technique for systems, but I guess we don't have to elaborate on the notorious inaccuracy of the predictor :|*

So I finally gave up in using adaptive stepsizes in my programs (though I was able to successfully program a Runge-Kutta-Fehlberg for a single DE, yay. Quite useful, but not sufficient to my needs). I was reading certain textbooks about the ABM method and as far as I can understand, I am supposed to use the previous data from a normal Runge-Kutta which is somewhat easy to code, and the main advantage would be the number of evaluations is slashed by half (is what I understood correct?) Speed-wise this would be what I need, further this should allow me to use ridiculously small stepsizes without taking too long with the evaluations (at least, from what I understood), and lastly would be very advantageous with my calculator's limited variables.

So I finally gave up in using adaptive stepsizes in my programs (though I was able to successfully program a Runge-Kutta-Fehlberg for a single DE, yay. Quite useful, but not sufficient to my needs). I was reading certain textbooks about the ABM method and as far as I can understand, I am supposed to use the previous data from a normal Runge-Kutta which is somewhat easy to code, and the main advantage would be the number of evaluations is slashed by half (is what I understood correct?) Speed-wise this would be what I need, further this should allow me to use ridiculously small stepsizes without taking too long with the evaluations (at least, from what I understood), and lastly would be very advantageous with my calculator's limited variables.

Since I already have two separate running third and fourth order Runge-Kutta programs already for systems of 4 DE's the initial values isn't much of a problem. I was also able to run an Adams-Bashforth-Moulton iteration for a single DE in Excel (which would be a fair practice for me in preparation of coding it). The remaining thing is I don't know how to run an ABM iteration with systems of equations. Can someone refer me, or give me something that could teach me how to, or at least a working example that I can emulate? I have no clue on how to start.

Sorry for the gigantic wall of text, but I just had to tell it, lol. Thanks and more power guys :]