Analysis for two-dimensional inverse quasilinear parabolic problem by Fourier method

Figures & data

Figure 1. Domain .

Figure 2. The accurate and numerical solutions of . The exact solution is shown with dashes line.

Figure 3. The numerical solution of .

Table 1. The relative errors for the functions and in different step sizes.

Step sizes		Relative error for		Relative error for
σ	τ					Time in seconds
0.0393	0.005	0.02	0.0202	0.012	0.010	3.9
0.0393	0.01	0.04	0.0408	0.0121	0.0148	3.1
0.0196	0.01	0.013	0.0122	0.01	0.011	9
0.0196	0.005	0.018	0.0182	0.006	0.007	24.4

Table 2. The relative errors for the functions and in different expected tolerance.

Prescribed tolerance		Relative error in
for	for			CPU in sec.
		0.08	0.05	2.1
		0.02	0.01	3.9
		0.018	0.09	3.2
		0.004	0.005	38.4

Table 3. The relative errors with some noisy data for the functions and in .

0% noisy data	0.02	0.01
1% noisy data	0.032	0.02
5% noisy data	0.058	0.081
10% noisy data	0.074	0.098

Table 4. The relative errors with some noisy data for the functions and in .

0% noisy data	0.014	0.079
1% noisy data	0.021	0.092
5% noisy data	0.053	0.12
10% noisy data	0.081	0.18

Figure 4. The accurate and numerical solutions of . The exact solution is shown with dashes line.

Figure 5. The numerical solution of .