HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 547

Here we are trying to obtain the value of y(2) given y(0) = 1. With the Soln: Final field highlighted, press @SOLVE. You can check that a solution takes about 6 seconds, while in the previous first-order example the solution was almost instantaneous. Press $ to cancel the calculation. This is an example of a stiff ordinary differential equation. A stiff ODE is one whose general solution contains components that vary at widely different rates under the same increment in the independent variable. In this particular case, the general solution, y(t) = 1+ t +C⋅e100t, contains the components 't' and 'C⋅e100t', which vary at very different rates, except for the cases C=0 or C≈0 (e.g., for C = 1, t =0.1, C⋅e100t =22026). The calculator's ODE numerical solver allows for the solution of stiff ODEs by selecting the option _Stiff in the SOLVE Y'(T) = F(T,Y) screen. With this option selected you need to provide the values of ∂f/∂y and ∂f/∂t. For the case under consideration ∂f/∂y = -100 and ∂f/∂t = 100. Enter those values in the corresponding fields of the SOLVE Y'(T) = F(T,Y) screen: When done, move the cursor to the Soln:Final field and press @SOLVE. This time, the solution in produced in about 1 second. Press @EDIT to see the solution: 2.9999999999, i.e., 3.0. Note: The option Stiff is also available for graphical solutions of differential equations. Numerical solution to ODEs with the SOLVE/DIFF menu The SOLVE soft menu is activated by using 74 MENU in RPN mode. This menu is presented in detail in Chapter 6. One of the sub-menus, DIFF, Page 16-69