Identifying an unknown source term in radial heat conduction

Figures & data

Figure 1. The comparison between the exact source function and the numerical ones with N = 1 and p = 2 for various levels of noise in the data, for Example 1.

Table 1. Relative error RRMSE(f) with ϵ = 1%, M = 31 for Example 1.

N	1	2	3	4	5	6	7	8
RRMSE(f)	0.0022	0.0079	0.0261	0.0195	0.0660	0.1948	0.3780	0.3286

Table 2. Relative error RRMSE(f) with ϵ = 1%, N = 1 for Example 1.

M	11	31	51	81	101	201	301	401
RRMSE(f)	0.0091	0.0022	0.0025	0.0024	0.0031	0.0020	0.0020	0.0028

Table 3. The influence of different p on α with ϵ = 1% for Example 1.

p				1	2	3
α	25.9760	25.4262	24.3266	22.1275	18.9005	13.3309

Figure 2. The comparison between the exact source function and the numerical ones with N = 5, p = 2 for ϵ = 1% and N = 4, p = 2 for ϵ = 10%, for Example 2.

Figure 3. The comparison between the exact source function and the numerical ones with N = 6, p = 2 for ϵ = 0.1% and N = 4, p = 2 for ϵ = 0.5%, for Example 3.

Figure 4. The comparison between the exact source function and the numerical ones with N = 6, p = 2 for ϵ = 0.1% and N = 4, p = 2 for ϵ = 0.5%, for Example 4.

Table 4. Relative error RRMSE(f) with ϵ = 1%, N = 5 for Example 2.

M	11	31	51	81	101	201	301	401
RRMSE(f)	0.2562	0.0874	0.0877	0.0797	0.0668	0.0686	0.0736	0.0746

Table 5. Relative error RRMSE(f) with ϵ = 0.1%, N = 6 for Example 3.

M	11	31	51	81	101	201	301	401
RRMSE(f)	0.5734	0.1465	0.1050	0.0842	0.1054	0.0820	0.0885	0.0898

Table 6. Relative error RRMSE(f) with ϵ = 0.1%, N = 6 for Example 4.

M	11	31	51	81	101	201	301	401
RRMSE(f)	0.5600	0.3277	0.3379	0.3186	0.3209	0.3382	0.3074	0.3175