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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Example 1: convection diffusion equation ( 51 ) at the point (0.5,0.5)

From: A new compact high order off-step discretization for the system of 2D quasi-linear elliptic partial differential equations

h

 

Proposed O( h 4 )-methods

O( h 2 )-Methods

β = 10

β = 50

β = 10

β = 50

1/8

u

6.4316(−01)

9.0714(−01)

6.4284(−01)

Diverges

u x

−5.0091(−01)

−1.8812(−01)

−5.1892(−01)

Diverges

u y

1.0190(−12)

1.8459(−13)

−1.1529(−12)

Diverges

1/16

u

6.4286(−01)

9.0637(−01)

6.4275(−01)

9.0666(−01)

u x

−5.0104(−01)

−1.7821(−01)

−5.0464(−01)

−1.7790(−01)

u y

2.2231(−12)

4.5889(−15)

−3.1806(−12)

3.4461(−13)

1/32

u

6.4284(−01)

9.0637(−01)

6.4281(−01)

9.0644(−01)

u x

−5.0105(−01)

−1.7821(−01)

−5.0190(−01)

−1.7808(−01)

u y

4.4296(−12)

6.8094(−15)

−6.4109(−12)

1.7764(−15)

1/64

u

6.4284(−01)

9.0637(−01)

6.4283(−01)

9.0639(−01)

u x

−5.0105(−01)

−1.7821(−01)

−5.0126(−01)

−1.7818(−01)

u y

8.5484(−12)

4.7370(−15)

−1.2545(−11)

1.4211(−14)

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