Compare your results with the analytical solution at x = 0.3 and determine the percentage error in each case.
Repeat Problem 4.4 using the Crank-Nicolson method. Compare your results with those obtained with the explicit method. Problem 4.4 Solve Eq. (4.2.4) subject to the following boundary and initial conditions: with the explicit method discussed in subsection 4.4.1 for values of t = 0.005, 0.01, 0.02, 0.10, with a = 0.2, for three different spacings in t. Compare your results with the analytical solution at x = 0.3 and determine the percentage error in each case. Discuss the accuracy of the results, the behavior of the solutions and the importance of the ratio in each case.
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