Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 5 A comparison of maximum error \((\Vert \cdot \Vert _{\infty })\) and Euclidean norm \((\Vert \cdot \Vert _{2})\) at \(T=1\) for problem-2

From: A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection–diffusion equation

N	τ = 1.25 × 10⁻³,γ = 0.3
	CBSCM [21]		MCTB-DQM [25]		Proposed method
	\(\Vert \cdot \Vert _{\infty }\)	\(\Vert \cdot \Vert _{2}\)	\(\Vert \cdot \Vert _{\infty }\)	\(\Vert \cdot \Vert _{2}\)	\(\Vert \cdot \Vert _{\infty }\)	\(\Vert \cdot \Vert _{2}\)	Order	CPU time
08	4.8273e−02	3.4134e−02	1.5762e−02	9.4300e−03	2.2761e−05	5.6903e−06	…	6.08404
16	1.2351e−02	8.7334e−03	2.1670e−03	1.1924e−03	7.4956e−06	1.3251e−06	1.60246	8.01845
32	3.1048e−03	2.1955e−03	2.8541e−04	1.5040e−04	1.7463e−06	2.1829e−07	2.1017	15.3193
64	7.7721e−04	5.4957e−04	3.6701e−05	1.8925e−05	1.3761e−07	1.2163e−08	3.6656	34.5386
128	1.9430e−04	1.3739e−04	4.6559e−06	2.3752e−06	2.2313e−08	1.3945e−09	2.62468	93.4914

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