Extend Example 3 as follows.(a) Verify the values in Table 21.13 and show them graphically as in Fig. 452.

Data from Table 21.13

Fig 452

(b) Compute and graph Euler values for h near the ?critical? h = 0.18 to determine more exactly when instability starts.

(c) Compute and graph RK values for values of h between 0.2 and 0.3 to find h for which the RK approximation begins to increase away from the exact solution.

(d) Compute and graph backward Euler values for large h; confirm stability and investigate the error increase for growing h.

X BEM h = 0.2 0.0 2.00000 0.2 1.36667 0.4 1.20556 0.6 1.21574 0.8 1.29460 1.0 1.40599 1.2 1.53627 1.4 1.67954 1.6 1.83272 1.8 1.99386 2.0 2.16152 BEM h = 0.4 2.00000 1.31429 1.35020 1.57243 1.86191 Euler h = 0.1 Euler h = 0.2 RK h = 0.2 2.00000 2.00000 1.01000 0.00000 1.56100 2.04000 1.13144 0.11200 1.23047 2.20960 1.34868 0.32768 1.48243 2.46214 1.62877 0.60972 1.78530 2.76777 1.80205 1.95009 0.93422 1.96535 2.13536 2.18625 2.12158 3.10737 RK h = 0.3 2.00000 1.35207 1.18144 1.18585 3.03947 1.26168 1.37200 1.50257 5.07569 1.64706 2.00000 8.72329 Exact 2.00000 1.15407 1.08864 1.15129 1.24966 1.36792 1.50120 1.64660 1.80190 1.96530 2.13534