Solved: CAS EXPERIMENT. Backward Euler and Stiffness.

Chapter 21, Problem 21.1.56

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Backward Euler and Stiffness. Extend Example 4 as follows.

(a) Verify the values in Table 21.14 and show them graphically as in Fig. 451.

(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.

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