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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)