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Theory and Modern Applications

Table 1 Example  1 : Case 1.1(a)(i): 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 [ 23 ]

Method given in [ 5 ]

Proposed method ( 3.6 )

0.1

0.001

1.11(–16)

5.55(–16)

5.55(–17)

0.005

9.43(–16)

1.77(–15)

7.77(–16)

0.010

4.21(–15)

2.55(–15)

3.13(–14)

0.5

0.001

1.11(–16)

3.88(–16)

1.66(–16)

0.005

4.44(–16)

2.60(–15)

1.38(–15)

0.010

1.66(–16)

4.99(–15)

8.16(–15)

0.9

0.001

0

1.05(–15)

5.55(–17)

0.005

1.99(–15)

3.44(–15)

0

0.010

5.05(–15)

5.16(–15)

4.44(–16)