ABSTRACT
The final results presented for the BTCS method are a parametric study in which the value of T(OA, 5.0) is calculated using values of fu: = 0.1, 0.05, 0.025, and 0.0125 cm, for values of d = 0.5, 1.0,2.0, and 5.0. The value of!1t for each solution is determined by the specified values of fu: and d. The exact solution is 1'(0.5,5.0) = 47.1255 C. The results are presented in Table 10.5. The truncation error of the BTCS method is OeM) + O(~). For a constant value of d, !1t = d fu:2 /ri.. Thus, as fu: is successively halved, !1t is quartered. Consequently, both the O(!1t) error term and the O(~) error term, and thus the total error, should decrease by a factor of approximately 4 as fu: is halved for a constant value of d. This result is clearly evident from the results presented in Table 10.5.
