Use the program from Exercise 7.11 to solve the diffusion problem Find, in particular, the value u(L2/4). (Hint: Scale the problem first.) Exercise 7.11 . The exercise is similar to Exercise 7.10, but...

Use the program from Exercise 7.11 to solve the diffusion problem

Find, in particular, the value u(L2/4). (Hint: Scale the problem first.)

Exercise 7.11

. The exercise is similar to Exercise 7.10, but now you should implement Algorithm 7.2.

Exercise 7.10

Write a program that implements Algorithm 7.1 in your favorite computer language. Note that if the arrays in your language cannot start at 0, you should rewrite the algorithm as suggested in Exercise 7.9. Use test problems from Sect. 7.4.4 to test your program.

Exercise 7.9

Algorithm 7.1 is easy to implement in a computer program if the computer language has arrays whose first index is 0. All languages with some inheritance from C (e.g., C++, Java, C#, Perl, Python, Ruby) have this feature. Some languages (Matlab, for instance) use index 1 for the first element in an array. You should then rewrite Algorithm 7.1 so that the index in space (usually called i in this book) runs from 1 to n C 1 and not from 0 to n. (This rewrite might sound trivial, but a simple change from i to i C 1 very often causes errors in programs.)