Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Comparison of estimated maximum pointwise errors of Example 1 for \(\pmb{N = 4}\) , \(\pmb{T=1}\) at \(\pmb{t=1}\) and different values of x

From: Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method

		x
		0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
Δt = 0.01	SMLP	1.9 × 10⁻³	3.4 × 10⁻³	4.4 × 10⁻³	5.1 × 10⁻³	5.3 × 10⁻³	5.1 × 10⁻³	4.4 × 10⁻³	3.4 × 10⁻³	1.9 × 10⁻³
Δt = 0.01	SMTR	7.6 × 10⁻⁴	8.7 × 10⁻⁴	8.9 × 10⁻⁴	9.1 × 10⁻⁴	9.3 × 10⁻⁴	9.2 × 10⁻⁴	8.6 × 10⁻⁴	7.5 × 10⁻⁴	6.7 × 10⁻⁴
Δt = 0.001	SMLP	4.1 × 10⁻⁴	6.1 × 10⁻⁴	5.3 × 10⁻⁴	4.9 × 10⁻⁴	4.9 × 10⁻⁴	4.9 × 10⁻⁴	5.3 × 10⁻⁴	6.1 × 10⁻⁴	4.1 × 10⁻⁴
Δt = 0.001	SMTR	1.2 × 10⁻⁴	1.8 × 10⁻⁴	1.4 × 10⁻⁴	2.1 × 10⁻⁴	9.2 × 10⁻⁵	9.6 × 10⁻⁵	8.9 × 10⁻⁵	1.6 × 10⁻⁴	2.3 × 10⁻⁴
Δt = 0.0001	TPEM	7.5 × 10⁻³	7.5 × 10⁻³	7.6 × 10⁻³	7.4 × 10⁻³	7.5 × 10⁻³	7.4 × 10⁻³	7.3 × 10⁻³	7.7 × 10⁻³	7.8 × 10⁻³
	TPIM	7.1 × 10⁻³	7.2 × 10⁻³	7.4 × 10⁻³	7.5 × 10⁻³	7.5 × 10⁻³	7.3 × 10⁻³	7.2 × 10⁻³	7.4 × 10⁻³	7.6 × 10⁻³
	CNM	5.1 × 10⁻³	5.2 × 10⁻³	5.3 × 10⁻³	5.2 × 10⁻³	5.4 × 10⁻³	5.3 × 10⁻³	5.5 × 10⁻³	5.3 × 10⁻³	5.2 × 10⁻³
	CM	6.2 × 10⁻⁴	6.1 × 10⁻⁴	6.5 × 10⁻⁴	6.6 × 10⁻⁵	6.6 × 10⁻⁵	6.6 × 10⁻⁵	6.4 × 10⁻⁴	6.5 × 10⁻⁴	6.4 × 10⁻⁴
	SMLP	2.6 × 10⁻⁴	3.1 × 10⁻⁴	1.3 × 10⁻⁴	1.1 × 10⁻⁵	1.7 × 10⁻⁵	1.1 × 10⁻⁵	1.3 × 10⁻⁴	3.1 × 10⁻⁴	2.6 × 10⁻⁴
	SMTR	7.5 × 10⁻⁵	8.1 × 10⁻⁵	5.7 × 10⁻⁵	9.2 × 10⁻⁶	9.5 × 10⁻⁶	9.1 × 10⁻⁶	7.8 × 10⁻⁵	8.6 × 10⁻⁵	8.2 × 10⁻⁵

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