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10 JEAN-DAVID BENAMOU, BRITTANY D. FROESE, AND ADAM M. OBERMAN(a)fig:errinf1(b)fig:time1Figure 2. Convergence results for u(x, y) = exp(x 2 +y 2N × N grid. (a) Error versus N. (b) Total CPU time.2)on anfig:ex1table:ex1_2N Iterations CPU Time (sec)(M1) (M2) (M1) (M2)21 1014 54 .9 0.181 14621 59 39.8 3.4141 42746 60 350.0 11.7201 84611 60 1540.0 27.2261 — 65 — 57.8......341 — 65 — 118.0421 — 78 — 249.0501 — 151 — 804.0581 — 284 — 2120.0Table ( 2. ) Computation times for the exact solution u(x, y) =exp x 2 +y 2on an N × N grid.2N 21 61 101 141 181 221∥∥u − u (N)∥ ∥∞5.5 × 10 −4 1.1 × 10 −4 5.0 × 10 −5 3.0 × 10 −5 2.1 × 10 −5 1.5 × 10 −5table:ex9Table 3. Errors for the exact solution u(x, y) = 2√ 23 (x2 + y 2 ) 3/4on an N × N grid. Results are the same for both methods.sec:noisy5.1. Noisy data. We now return to the first example we considered, with exactsolution( x 2 + y 2 )u(x, y) = exp, f(x, y) = (1 + x 2 + y 2 ) exp(x 2 + y 2 ),2