Page 273 - Excel for Scientists and Engineers: Numerical Methods

250 EXCEL: NUMERICAL METHODS

To solve the second-order differential equation

-- d2Y y=o (11-6)
dx
we express it as two first-order differential equations:
dz
_- y=o (1 1-7)
dx
and

(1 1-8)

The initial calculation, using a trial value of z = 0, is shown in Figure 1 1-6.

Figure 11-6. Preparing to solve the differential equation y" -y = 0
by the shooting method. The initial boundary values
and the initial trial value of the derivative are in bold.
(folder 'Chapter 1 1 Examples', workbook 'ODE-BVP', worksheet 'y"-y'O (Euler)')

As before, we will use Euler's method to develop an inaccurate but simple
solution to the problem, then obtain a more accurate result by using the RK
method. Euler's method formulas were used to calculate the values of y and z.
The formulas used in cells C7 and D7 are, respectively
=B6*(A7-A6)

and
=D6+C7