Problem 27.2

Example 2 - Page #808, Problem 27.2

Runge Kutta

Starting X value: Left boundary endpoint

Left boundary endpoint

Final X Value: Right boundary endpoint

Right boundary endpoint

Step Size:

T(X-Start): Initial T value at left boundary endpoint

Initial T value at left boundary endpoint

Initial z: Guess for initial slope

Guess for initial slope

Equations

Result:

Linear Interpolation

T₁(z1):

Runge Kutta result for guess z1

T₂(z2):

Runge Kutta result for guess z2

z₁:

1st initial guess for slope

z₂:

2nd initial guess for slope

Beta:

Actual T value at right boundary endpoint

Linear Interpolation Formula

Result: