Solving systems of firstorder differential equations

09162022, 04:49 PM
Post: #1




Solving systems of firstorder differential equations
This HP Prime program demonstrates how to interact with an rkf78 subroutine which solves firstorder systems of ordinary differential equations. This is an HPPL implementation of the RungeKuttaFehlberg method of order 7 with an 8th order error estimate. This estimate is used to determine the variable step size required to satisfy a userdefined "convergence" criterion.
Here's the source code for a typical system of firstorder differential equations included in this demo program. This code implements Keplerian (unperturbed) orbital motion. keqm (t, y) // first order equations of orbital motion // Keplerian motion  no perturbations // input // t = simulation time (seconds) // y = state vector (kilometers and kilometers/second) // output // ydot = integration vector (kilometers/second/second) ///////////////////////////// BEGIN LOCAL rmag, rcubed; LOCAL ydot := [0, 0, 0, 0, 0, 0]; rmag := sqrt(y(1) * y(1) + y(2) * y(2) + y(3) * y(3)); rcubed := rmag * rmag * rmag; // integration vector ydot(1) := y(4); ydot(2) := y(5); ydot(3) := y(6); ydot(4) := emu * y(1) / rcubed; ydot(5) := emu * y(2) / rcubed; ydot(6) := emu * y(3) / rcubed; return ydot; END; The main program defines typical orbital elements of an Earth satellite and propagates the orbit for 10 Keplerian periods. The errors between the initial and final conditions indicate how well the algorithm performs. 

09242022, 03:46 PM
Post: #2




RE: Solving systems of firstorder differential equations
Software update
> moved rkf78 coefficients into the subroutine > clean up print statements to take advantage of \n new line feature 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)