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Theory and Modern Applications

Table 7 Example  1 : Case 1.3(a): Maximum absolute errors at \(\pmb{\delta = 1}\)

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

1.68(–11)

2.59(–12)

5.66(–13)

1.0

1.79(–11)

2.74(–12)

3.42(–13)

2.0

1.46(–11)

2.74(–12)

6.27(–13)

0.5

0.5

3.40(–12)

7.36(–13)

7.52(–14)

1.0

3.72(–12)

7.99(–13)

4.81(–14)

2.0

3.13(–12)

8.39(–13)

3.06(–14)

0.9

0.5

1.31(–11)

2.67(–12)

5.55(–17)

1.0

1.37(–11)

2.96(–12)

5.55(–17)

2.0

1.07(–11)

3.24(–12)

8.88(–16)