Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Comparisons of errors between the exponential θ -method and the Euler method

From: Numerical oscillations for first-order nonlinear delay differential equations in a hematopoiesis model

	Exponential θ-method						Euler method
	θ = 0.2		θ = 0.5		θ = 0.7		Euler method
	AE	RE	AE	RE	AE	RE	AE	RE
m = 7	0.0144	0.0112	0.0030	0.0023	0.0174	0.0135	0.0229	0.0177
m = 14	0.0085	0.0066	0.0010	7.8091e − 4	0.0080	0.0062	0.0140	0.0109
m = 28	0.0044	0.0034	5.1373e − 4	3.9864e − 4	0.0040	0.0031	0.0075	0.0058
m = 35	0.0035	0.0027	4.5459e − 4	3.5275e − 4	0.0032	0.0025	0.0060	0.0047
m = 70	0.0016	0.0013	3.7574e − 4	2.9156e − 4	0.0017	0.0013	0.0029	0.0023

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