HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 548

contains functions for the numerical solution of ordinary differential equations for use in programming. These functions are described next using RPN mode and system flag 117 set to SOFT menus. The functions provided by the SOLVE/DIFF menu are the following: Function RKF This function is used to compute the solution to an initial value problem for a first-order differential equation using the Runge-Kutta-Fehlbert 4th -5th order solution scheme. Suppose that the differential equation to be solved is given by dy/dx = f(x,y), with y = 0 at x = 0, and that you will allow a convergence criteria ε for the solution. You can also specify an increment in the independent variable, ∆x, to be used by the function. To run this function you will prepare your stack as follows: 3: {'x', 'y', 'f(x,y)'} 2: { ε ∆x } 1: xfinal The value in the first stack level is the value of the independent variable where you want to find your solution, i.e., you want to find, yfinal = fs(xfinal), where fs(x) represents the solution to the differential equation. The second stack level may contain only the value of ε, and the step ∆x will be taken as a small default value. After running function @@RKF@@, the stack will show the lines: 2: {'x', 'y', 'f(x,y)'} 1: ε The value of the solution, yfinal, will be available in variable @@@y@@@. This function is appropriate for programming since it leaves the differential equation specifications and the tolerance in the stack ready for a new solution. Notice that the solution uses the initial conditions x = 0 at y = 0. If, your actual initial solutions are x = xinit at y = yinit, you can always add these values to the solution provided by RKF, keeping in mind the following relationship: Page 16-70