Numerical Solution To Odes With The Solve/Diff Menu - HP 49g+ User Manual

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Here we are trying to obtain the value of y(2) given y(0) = 1. With the

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⋅e

, contains the components 't'

', which vary at very different rates, except for the cases C=0 or

C≈0 (e.g., for C = 1, t =0.1, C⋅e

The calculator's ODE numerical solver allows for the solution of stiff ODEs by

selecting the option

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)

field and press @SOLVE.

When done, move the cursor to the

Press @EDIT to see the

time, the solution in produced in about 1 second.

solution: 2.9999999999, i.e., 3.0.

Note: The option

is also available for graphical solutions of differential

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,