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Theory and Modern Applications

Table 8 Example  1 : Case 1.3(b): Maximum absolute errors at \(\pmb{\delta = 2}\)

From: High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations

x

t

Method given in [ 25 ]

Method given in [ 5 ]

Proposed method ( 3.6 )

0.1

0.5

4.49(–11)

2.83(–11)

6.14(–12)

1.0

4.19(–11)

2.78(–11)

7.28(–12)

2.0

2.70(–11)

2.41(–11)

9.17(–12)

0.5

0.5

8.13(–12)

8.42(–12)

2.24(–13)

1.0

7.72(–12)

8.50(–12)

2.71(–13)

2.0

4.77(–12)

7.85(–12)

3.55(–13)

0.9

0.5

3.55(–11)

3.13(–11)

3.33(–16)

1.0

3.23(–11)

3.23(–11)

3.33(–16)

2.0

1.98(–11)

3.14(–11)

4.44(–16)