Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Comparison of LTVIM, HPM [17], HPTM [18], RPSM, and HATM [20] on Example 4.1. Here \(\alpha = 1\) is used for all methods

From: A numerical method using Laplace-like transform and variational theory for solving time-fractional nonlinear partial differential equations with proportional delay

x	t	Absolute error
x	t	LTVIM	HPM [17], HPTM [18], RPSM and HATM [20]
0.25	0.25	5.78490 × 10⁻⁷	2.12240 × 10⁻⁶
	0.50	1.99999 × 10⁻⁵	7.09428 × 10⁻⁵
	0.75	1.64394 × 10⁻⁴	5.63480 × 10⁻⁴
	1	7.51289 × 10⁻⁴	2.48712 × 10⁻³
0.50	0.25	1.15698 × 10⁻⁶	4.24500 × 10⁻⁶
	0.50	3.99999 × 10⁻⁵	1.41885 × 10⁻⁵
	0.75	3.28789 × 10⁻⁴	1.12696 × 10⁻³
	1	1.50258 × 10⁻³	4.97424 × 10⁻³
0.75	0.25	1.73547 × 10⁻⁶	6.36750 × 10⁻⁶
	0.50	5.99999 × 10⁻⁵	2.12828 × 10⁻⁴
	0.75	4.93183 × 10⁻⁴	1.69044 × 10⁻³
	1	2.25387 × 10⁻³	7.46137 × 10⁻³

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