Figure 2

The exact (37) and approximate \(z(r,t)\), and absolute errors with various grid sizes \(M=N\): (a) 10, (b) 20, (c) 40, and (d) 80 for the forward problem
The exact (37) and approximate \(z(r,t)\), and absolute errors with various grid sizes \(M=N\): (a) 10, (b) 20, (c) 40, and (d) 80 for the forward problem