Hp 49g+ User Manual download pdf (Page 534)

100

101

Page 16-60

0 HERMITE, result: 1, i.e., H

= 1.

1 HERMITE, result: ’2*X’, i.e., H

= 2x.

2 HERMITE, result: ’4*X^2-2’, i.e., H

= 4x

-2.

3 HERMITE, result: ’8*X^3-12*X’, i.e., H

= 8x

-12x.

Numerical and graphical solutions to ODEs

Differential equations that cannot be solved analytically can be solved

numerically or graphically as illustrated below.

Numerical solution of first-order ODE

Through the use of the numerical solver (‚Ï), you can access an input

form that lets you solve first-order, linear ordinary differential equations. The

use of this feature is presented using the following example. The method used

in the solution is a fourth-order Runge-Kutta algorithm preprogrammed in the

calculator.

Example 1

-- Suppose we want to solve the differential equation, dv/dt = -1.5

1/2

, with v = 4 at t = 0. We are asked to find v for t = 2.

First, create the expression defining the derivative and store it into variable

EQ. The figure to the left shows the ALG mode command, while the right-

hand side figure shows the RPN stack before pressing K.

Then, enter the NUMERICAL SOLVER environment and select the differential

equation solver: ‚Ï˜ @@@OK@@@ . Enter the following parameters:

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