New High-Order Compact ADI Algorithms for 3D Nonlinear Time-Fractional Convection-Diffusion Equation

Table 6

𝑇=0.01 and 𝑀=100 with different 𝛼 and 𝑁 using Algorithm 2 for Problem 6.

	𝑁	5	10	20	30	40
𝛼=0.2	𝐿^∞-error	2.7154𝑒−4	1.8711𝑒−5	1.1750𝑒−6	2.2446𝑒−7	6.4536𝑒−8
	𝐿^∞-rate	—	3.8592	3.9932	4.0825	4.3329
	𝐿^2-error	6.3987𝑒−5	4.5423𝑒−6	3.0190𝑒−7	5.9489𝑒−8	1.7738𝑒−8
	𝐿^2-rate	—	3.8163	3.9113	4.0060	4.2064
𝛼=0.5	𝐿^∞-error	2.4981𝑒−4	1.7177𝑒−5	1.0951𝑒−6	2.2343𝑒−7	7.2771𝑒−8
	𝐿^∞-rate	—	3.8623	3.9713	3.9202	3.8994
	𝐿^2-error	5.8471𝑒−5	4.1544𝑒−6	2.7991𝑒−7	5.8491𝑒−8	1.9056𝑒−8
	𝐿^2-rate	—	3.8150	3.8916	3.8612	3.8983
𝛼=0.8	𝐿^∞-error	2.1863𝑒−4	1.5586𝑒−5	1.0322𝑒−6	2.1189𝑒−7	6.8378𝑒−8
	𝐿^∞-rate	—	3.8102	3.9165	3.9051	3.9315
	𝐿^2-error	5.2327𝑒−5	3.7485𝑒−6	2.4905𝑒−7	5.0023𝑒−8	1.6021𝑒−8
	𝐿^2-rate	—	3.8023	3.9118	3.9588	3.9578