A backward problem for distributed order diffusion equation: uniqueness and numerical solution

Figures & data

Figure 1. inversion solution for Example 5.1.

Figure 2. inversion solution for Example 5.2.

Table 1. Inversion results for the four numerical examples with different relative errors.

Example	δ	$\overline{\iota }$	$\frac{\Vert {\phi }_k({\beta }_{\overline{\iota }})-{\phi }^{\star }{\Vert }_{L^2(0,l)}}{\Vert {\phi }^{\star }{\Vert }_{L^2(0,l)}}$
Example 5.1	0.1%	5	3.27%
	0.5%	4	3.83%
	1%	4	4.62%
	2%	3	5.11%
Example 5.2	0.1%	5	5.45%
	0.5%	4	5.69%
	1%	4	7.35%
	2%	4	7.73%
Example 5.3	0.1%	5	6.39%
	0.5%	4	7.22%
	1%	4	7.92%
	2%	3	9.13%
Example 5.4	0.1%	5	3.70%
	0.5%	5	3.90%
	1%	4	5.67%
	2%	4	6.28%

Figure 3. inversion solution for Example 5.3.

Figure 4. inversion solution for Example 5.4.