Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Example 1: The global relative errors

From: A new two-level implicit scheme of order two in time and four in space based on half-step spline in compression approximations for unsteady 1D quasi-linear biharmonic equations

(a)
t	Proposed method (3.39)–(3.40)	Method discussed in [18]	Method discussed in [15]	Method discussed in [13]
1	1.9827(−05)	6.0297(−05)	3.8173(−04)	6.7923(−04)
2	3.1204(−05)	9.9303(−05)	5.5114(−04)	1.1503(−03)
3	8.2856(−05)	1.3064(−04)	7.0398(−04)	1.5941(−03)
4	8.5826(−05)	1.6060(−04)	8.6366(−04)	2.0075(−03)

(b)
t	L + 1 = 200		L + 1 = 300		L + 1 = 400
t	Proposed method (3.39)–(3.40)	Method discussed in [15]	Proposed method (3.39)–(3.40)	Method discussed in [15]	Proposed method (3.39)–(3.40)	Method discussed in [15]
1	3.4024(−05)	2.1335(−04)	2.5260(−05)	1.2335(−04)	2.3821(−05)	6.6956(−05)
2	5.8546(−05)	3.0874(−04)	4.6256(−05)	1.6780(−04)	2.6792(−05)	9.6417(−05)
3	8.0178(−05)	3.9500(−04)	6.5287(−05)	2.0791(−04)	4.5023(−05)	1.0947(−04)
4	9.8195(−05)	4.8479(−04)	8.2460(−05)	2.5018(−04)	8.0236(−05)	1.2600(−04)

Back to article page