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Theory and Modern Applications

Table 3 Comparison of absolute errors for Problem 2 when \(n=100\)

From: Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations

γ

Method in [21]

Proposed method

Δt = 0.000001, t = 0.0001

Δt = 0.01, t = 1

\(L_{\infty }\)

\(L_{2}\)

\(L_{\infty }\)

\(L_{2}\)

0.25

9.6400 × 10−7

6.8165 × 10−8

9.5143 × 10−9

9.2399 × 10−9

0.50

9.9135 × 10−7

7.0099 × 10−8

8.9541 × 10−9

8.4093 × 10−9

0.75

9.9997 × 10−7

7.0709 × 10−8

9.7525 × 10−9

8.2487 × 10−9

1.00

1.0000 × 10−6

7.0711 × 10−8

9.8911 × 10−9

9.0927 × 10−9