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Source strength identification problem for the three-dimensional inverse heat conduction equations

Tao MinDepartment of Applied Mathematics, Xi’an University of Technology, Xi’an, People’s Republic of ChinaCorrespondence[email protected]
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Shunquan ZangDepartment of Applied Mathematics, Xi’an University of Technology, Xi’an, People’s Republic of China;School of Science, Xi’an University of Posts and Telecommunications, Xi’an, People’s Republic of ChinaView further author information

Shengnan ChenDepartment of Applied Mathematics, Xi’an University of Technology, Xi’an, People’s Republic of ChinaView further author information

Figures & data

Table 1. Additional values of $u (0.25, 0.25, 0.25, t_{i})$ .

Display Table

Figure 1. Comparison of exact and numerical solutions using Tikhonov regularization with $σ = 0$ .

Figure 2. Comparison of exact and numerical solutions using TSVD with $σ = 0$ .

Table 2. $L_{\infty}$ error norm and RE for $g (t)$ , with $σ = 0$ .

Display Table

Figure 3. Comparison of exact and numerical solutions using Tikhonov regularization with $σ =$ 2.16583542×10⁻⁵.

Figure 3. Comparison of exact and numerical solutions using Tikhonov regularization with σ=2.16583542×10−5.

Figure 4. Comparison of exact and numerical solutions using TSVD with $σ =$ 2.16583542×10⁻⁵.

Figure 4. Comparison of exact and numerical solutions using TSVD with σ=2.16583542×10−5.

Table 3. $L_{\infty}$ error norm and RE for $g (t)$ , with $σ =$ 2.16583542×10⁻⁵.

Display Table

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Source strength identification problem for the three-dimensional inverse heat conduction equations

Table 1. Additional values of $u (0.25, 0.25, 0.25, t_{i})$ .

Table 2. $L_{\infty}$ error norm and RE for $g (t)$ , with $σ = 0$ .

Table 3. $L_{\infty}$ error norm and RE for $g (t)$ , with $σ =$ 2.16583542×10⁻⁵.

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Source strength identification problem for the three-dimensional inverse heat conduction equations

Figures & data

Table 1. Additional values of u(0.25,0.25,0.25,ti).

Table 2. L∞ error norm and RE for g(t), with σ=0.

Table 3. L∞ error norm and RE for g(t), with σ=2.16583542×10−5.

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Table 1. Additional values of $u (0.25, 0.25, 0.25, t_{i})$ .

Table 2. $L_{\infty}$ error norm and RE for $g (t)$ , with $σ = 0$ .

Table 3. $L_{\infty}$ error norm and RE for $g (t)$ , with $σ =$ 2.16583542×10⁻⁵.