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

Table 7

Maximum absolute errors and rate in the computed solution, Example 10 with 𝜖=0.1.

ℎ=𝑘	UDS		CDS		EDS		EDS-RE
	Errors	Rate	Errors	Rate	Errors	Rate	Errors	Rate
1/8	2.41𝑒−1		7.50𝑒−2		7.93𝑒−3		3.51𝑒−5
1/16	1.39𝑒−1	0.79	1.65𝑒−2	2.19	2.02𝑒−3	1.96	2.16𝑒−6	3.93
1/32	7.76𝑒−2	0.84	4.19𝑒−3	1.98	5.09𝑒−4	1.99	1.32𝑒−7	3.98
1/64	4.11𝑒−2	0.92	1.04𝑒−3	2.01	1.28𝑒−4	2.00	8.16𝑒−9	4.00
1/128	2.12𝑒−2	0.96	2.59𝑒−4	2.00	3.19𝑒−5	2.00

Note. The convergence criterion of the Gauss Seidel iteration for EDS-RE scheme is chosen to be 3×10⁻¹⁶ to obtain highly accurate results.