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Theory and Modern Applications

Table 1a Errors and order for UM-FOCS in Example 5.1

From: Exponential basis and exponential expanding grids third (fourth)-order compact schemes for nonlinear three-dimensional convection-diffusion-reaction equation

 

τ = 1.0

τ = 0.1

τ = 0.01

L + 1

\(\mathfrak {l}_{2}^{ ( I,J,K )}\)

\(\varTheta _{2}\)

\(\mathfrak {l}_{2}^{ ( I,J,K )}\)

\(\varTheta _{2}\)

\(\mathfrak {l}_{2}^{ ( I,J,K )}\)

\(\varTheta _{2}\)

4

5.67e–04

4.36e–02

1.02e+01

8

2.86e–05

4.3

2.82e–03

4.0

2.32e+00

2.1

16

6.55e–07

5.4

1.70e–04

4.0

4.65e–01

2.3