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Theory and Modern Applications

Table 14 Example  7 : Maximum absolute error at \(\pmb{\varepsilon = 1}\) , \(\pmb{\alpha_{1} = \beta_{1} = - 2}\) , \(\pmb{\alpha_{2} = \beta_{2} = 1}\) , \(\pmb{h = 2\pi /100}\) , \(\pmb{k = 0.01}\)

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

t

Proposed method ( 4.28 )

Method discussed in [ 11 ]

u

v

u

v

0.5

2.5045(–06)

2.5045(–06)

1.5168(–04)

1.5168(–04)

1.0

3.0373(–06)

3.0373(–06)

1.8397(–04)

1.8397(–04)

2.0

2.2330(–06)

2.2330(–06)

1.3525(–04)

1.3525(–04)

3.0

1.2296(–06)

1.2296(–06)

7.4601(–05)

7.4601(–05)