ABSTRACT
As an example of the shooting method with a derivative BC, let's solve Eq. (8.75). The implicit trapezoid method for this problem is presented in Example 8.1, Eqs. (8.23) and (8.24). Let (,(2 = 16.0 em-2, Ta = 0.0 C, and LU = 0.25 em. Let T(O.O) = 100.0 C and U(O.O) = T'(O.O) be the initial conditions at x = 0.0 em, and shoot for the boundary condition at x = 1.0em, 1"(1.0) = U(1.0) = O.OC/em. Let U(O.O)(l) = -405.0C/em and U(0.0)(2) = 395.0 Clem. The solution for these two values of U(O.O) are presented in Table 8.14 and Figure 8.13. For U(0.0)(l)=-405.0C/em, T'(I.O)(I)= -207.469136C/em, and for U(0.0)(2) = -395.0C/em, T'(I.OP) = 197.592593C/em. The final solution (obtained by superposition), the exact solution, and the errors are presented in Table 8.15. The final solution is also plotted in Figure 8.13.
