Fourier truncation method for the non-homogeneous time fractional backward heat conduction problem

Figures & data

Figure 1. Exact and truncated solution for different δ with $\alpha =0.05$.

Figure 2. Exact and truncated solution for different δ with $\alpha =0.2$.

Figure 3. Exact and truncated solution for different δ with $\alpha =0.4$.

Figure 4. Exact and truncated solution for different δ with $\alpha =0.6$.

Figure 5. Exact and truncated solution for different δ with $\alpha =0.8$.

Figure 6. Exact and truncated solution for different δ with $\alpha =0.95$.

Figure 7. Exact and truncated solution for different δ with $\alpha =0.05$.

Figure 8. Exact and truncated solution for different δ with $\alpha =0.2$.

Figure 9. Exact and truncated solution for different δ with $\alpha =0.4$.

Figure 10. Exact and truncated solution for different δ with $\alpha =0.6$.

Figure 11. Exact and truncated solution for different δ with $\alpha =0.8$.

Figure 12. Exact and truncated solution for different δ with $\alpha =0.95$.

Table 1. Relative and absolute error estimates for different δ and α values.

	$\alpha =0.05$		$\alpha =0.2$		$\alpha =0.4$
δ	REE	AEE	REE	AEE	REE	AEE
0.01	0.0650	0.0075	0.0650	0.0075	0.0650	0.0075
0.001	0.0146	0.0017	0.0146	0.0017	0.0146	0.0017
0.0001	0.0039	4.524e-04	0.0039	4.524e-04	0.0039	4.524e-04

Table 2. Relative and absolute error estimates for different δ and α values.

	$\alpha =0.6$		$\alpha =0.8$		$\alpha =0.95$
δ	REE	AEE	REE	AEE	REE	AEE
0.01	0.0651	0.0075	0.0651	0.0075	0.0651	0.0075
0.001	0.0146	0.0017	0.0147	0.0017	0.0147	0.0017
0.0001	0.0040	4.5247e-04	0.0040	4.5247e-04	0.0040	4.5249e-04

Table 3. Relative and absolute error estimates for different δ and α values.

	$\alpha =0.05$		$\alpha =0.2$		$\alpha =0.4$
δ	REE	AEE	REE	AEE	REE	AEE
0.01	0.0200	0.0023	0.0201	0.0023	0.0206	0.0023
0.001	0.0057	6.5269e-04	0.0057	6.5343e-04	0.0057	6.5275e-04
0.0001	0.0013	1.5159e-04	0.0013	1.5159e-04	0.0013	1.5159e-04

Table 4. Relative and absolute error estimates for different δ and α values.

	$\alpha =0.6$		$\alpha =0.8$		$\alpha =0.95$
δ	REE	AEE	REE	AEE	REE	AEE
0.01	0.0202	0.0023	0.0201	0.0023	0.0200	0.0023
0.001	0.0057	6.5277e-04	0.0057	6.5372e-04	0.0057	6.5495e-04
0.0001	0.0013	1.5159e-04	0.0013	1.5159e-04	0.0013	1.5159e-04