Inverse Estimates for Nonhomogeneous Backward Heat Problems

Table 6

𝑇=1, the analytical and numerical results for the 𝑓(𝑥_𝑗) in 𝑥_𝑗=0.1𝑗, where 𝛿=0.1.

𝑗	Exact 𝑓(𝑥𝑗)	Numerical 𝑓(𝑥𝑗)	|𝑓(𝑥𝑗)−𝑓(𝑥𝑗)|
1	0.309016994374947	0.308938263749532	7.8730625415413×10^−5
2	0.587785252292473	0.587635497743805	1.49754548667946×10^−4
3	0.809016994374947	0.808810874921651	2.06119453296294×10^−4
4	0.951056516295154	0.950814208345435	2.42307949718912×10^−4
5	1	0.999745222344235	2.54777655765204×10^−4
6	0.951056516295154	0.950814208345429	2.42307949724685×10^−4
7	0.809016994374947	0.808810874921642	2.06119453305731×10^−4
8	0.587785252292473	0.587635497743796	1.49754548676939×10^−4
9	0.309016994374948	0.308938263749526	7.87306254214082×10^−5
10	1.22464679914735×10^−16	6.12167393253357×10^−17	6.12479405893996×10^−17