Plot the solution, you can use software like Matlab to do this.

Class: Partial Differential Equations I

16.6 Characteristics and d'Alembert's Solution In this section, we will derive d'Alembert's solution of a wave problem on the real line. We will denote partial derivatives by subscripts, au/at=u, and a u/ax=uz. The problem we will solve is u =tu, for 00 0 and (x,0)= f(x), 4(x,0) = g(x) for -00 2 (12) 16.6 Characteristics and d'Alembert's Solution In this section, we will derive d'Alembert's solution of a wave problem on the real line. We will denote partial derivatives by subscripts, au/at=u, and a u/ax=uz. The problem we will solve is u =tu, for 00 0 and (x,0)= f(x), 4(x,0) = g(x) for -00 2 (12)