A New Way to Generate an Exponential Finite Difference Scheme for 2D Convection-Diffusion Equations

Table 1

Maximum absolute errors with Re = 1 (left) and Re = 100 (right), Example 7.

ℎ=𝑘	Re = 1			Re = 100
	UDS	CDS	EDS	UDS	CDS	EDS
1/8	3.57𝑒−3	8.05𝑒−5	1.55𝑒−15	2.66𝑒−7	—	1.21𝑒−22
1/16	1.87𝑒−3	2.03𝑒−5	6.83𝑒−15	2.45𝑒−4	—	2.96𝑒−21
1/32	9.63𝑒−4	5.12𝑒−6	2.70𝑒−14	7.70𝑒−3	—	1.03𝑒−18
1/64	4.87𝑒−4	1.28𝑒−6	1.03𝑒−13	3.03𝑒−2	1.70𝑒−2	4.19𝑒−17
1/128	2.44𝑒−4	3.20𝑒−7	4.06𝑒−13	3.22𝑒−2	6.68𝑒−3	2.10𝑒−16
1/256	1.23𝑒−4	8.00𝑒−8	1.58𝑒−12	2.01𝑒−2	1.64𝑒−3	9.42𝑒−16

— means CDS diverges for Re = 100 when the mesh size is big.