Different approaches for the solution of a backward heat conduction problem

Figures & data

TABLE I Error values for noiseless data – Eq. (40)

Estimation errors with noiseless data
Method employed	Triangular function	Semitriangular function
Alifanov	0.00756	0.01741
Quasi-Newton	0.02209	0.10155
Genetic algorithm	2.01913	5.89825
Genetic algorithm*	2.36247	5.57705

TABLE II Error values for noisy data – Eq. (40)

Estimation errors with noisy data
Method employed	Triangular function	Semitriangular function
Alifanov	0.12213	0.13708
Quasi-Newton	0.15272	0.26307
Genetic algorithm	0.10623	0.15315
Genetic algorithm*	0.15778	0.23324
Genetic algorithm†	0.11485	0.77282

FIGURE 1 Alifanov's approach solution for the triangular function without regularization.

FIGURE 2 Quasi-Newton method solution for the triangular function without regularization.

FIGURE 3 Genetic algorithm solution for the triangular function without regularization: epidemical operator nonactivated.

FIGURE 4 Genetic algorithm solution for the triangular function without regularization: epidemical operator activated.

FIGURE 5 Alifanov's approach solution for the semitriangular function without regularization.

FIGURE 6 Quasi-Newton method solution for the semitriangular function without regularization.

FIGURE 7 Genetic algorithm solution for the semitriangular function without regularization: epidemical operator nonactivated.

FIGURE 8 Genetic algorithm solution for the semitriangular function without regularization: epidemical operator activated.

FIGURE 9 Alifanov's approach solution for the triangular function.

FIGURE 10 Quasi-Newton method solution for the triangular function.

FIGURE 11 Genetic algorithm solution for the triangular function with the epidemical operator nonactivated.

FIGURE 12 Genetic algorithm solution for the triangular function with the epidemical operator activated.

FIGURE 13 Genetic algorithm solution for the triangular function with the first order Tikhonov regularization: epidemical operator nonactivated.

FIGURE 14 Alifanov's approach solution for the semitriangular function.

FIGURE 15 Quasi-Newton method solution for the semitriangular function.

FIGURE 16 Genetic algorithm solution for the semitriangular function with the epidemical operator nonactivated.

FIGURE 17 Genetic algorithm solution for the semitriangular function with the epidemical operator activated.

FIGURE 18 Genetic algorithm solution for the semitriangular function with the first order Tikhonov regularization: epidemical operator nonactivated.