Table 5 Comparing of numerical results/REFs using QLM-FSVLFs technique for \(\gamma =1.7,\sigma =0.7\), \(m,\lambda =1\), \(A=2\), \(K=6\), \(\alpha =1,1.7\), and various \(r\in [0,1]\).

From: Computational analysis of a class of singular nonlinear fractional multi-order heat conduction model of the human head

r

QLM-FSVLFs

PLSM21

\(h^{(6)}_{6,1}(r)\)

\({\mathbb {R}}_{6,1}^{(6)}(r)\)

\(h^{(6)}_{6,\frac{17}{10}}(r)\)

\({\mathbb {R}}_{6,\frac{17}{10}}^{(6)}(r)\)

\(\tilde{u}(r)\)

Error

0.0

1.18587014

\(0.0000_{-0}\)

1.186078708050383

\(0.0000_{-0}\)

1.18592781

\(0.000_{-0}\)

0.1

1.18480830

\(3.6771_{-3}\)

1.184762989665008

\(3.5729_{-9}\)

1.18482122

\(1.438_{-3}\)

0.2

1.18196899

\(1.9265_{-3}\)

1.181798785635447

\(4.9691_{-9}\)

1.18191175

\(3.193_{-4}\)

0.3

1.17772081

\(5.5686_{-4}\)

1.177537074846438

\(4.1642_{-9}\)

1.17761666

\(4.895_{-4}\)

0.4

1.17228067

\(5.7501_{-6}\)

1.172118584802979

\(2.2938_{-9}\)

1.17216020

\(6.580_{-6}\)

0.5

1.16576606

\(6.1427_{-5}\)

1.165624795848758

\(6.6587_{-10}\)

1.16564798

\(2.022_{-4}\)

0.6

1.15823600

\(1.3109_{-6}\)

1.158108073063764

\(4.6515_{-11}\)

1.15812382

\(5.054_{-5}\)

0.7

1.14972066

\(1.9547_{-5}\)

1.149603273305191

\(5.0383_{-11}\)

1.14960897

\(3.427_{-4}\)

0.8

1.14023972

\(5.4729_{-6}\)

1.140133388637926

\(3.2844_{-11}\)

1.14012396

\(1.437_{-4}\)

0.9

1.12980937

\(3.8068_{-6}\)

1.129712674036530

\(1.7034_{-11}\)

1.12969271

\(4.717_{-4}\)

1.0

1.11843798

\(6.5566_{-6}\)

1.118348529287161

\(1.1143_{-11}\)

1.11832927

\(3.310_{-5}\)

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