On Step Approximation for Roseau's Analytical Solution of Water Waves

Table 6

Comparison with the explicit solution of Roseau and the method of Evans and Linton [19] (most accurate solutions are bold).

𝐾, ε, β	0.1, 0.1, 0.1		1, 0.5, 1		0.1, 0.1, 1.5
	|𝑅|	|𝑇|	|𝑅|	|𝑇|	|𝑅|	|𝑇|
IEMM (𝑀=11,𝐿=0)	0.1144	1.7271	0.0748	1.0435	0.4747	1.5301
IEMM (𝑀=21,𝐿=0)	0.2857	1.6660	0.0056	1.0464	0.4723	1.5323
IEMM (𝑀=51,𝐿=0)	0.0046	1.7385	0.0066	1.0464	0.4791	1.5260
IEMM (𝑀=101,𝐿=0)	0.0015	1.7385	0.0071	1.0464	0.4802	1.5250
IEMM (𝑀=201,𝐿=0)	0.0017	1.7385	0.0073	1.0464	0.4807	1.5245
IEMM (𝑀=301,𝐿=0)	0.0017	1.7385	0.0073	1.0464	0.4809	1.5243
IEMM (𝑀=11,𝐿=3)	0.1128	1.7274	0.0757	1.0434	0.4751	1.5298
IEMM (𝑀=21,𝐿=3)	0.2853	1.6662	0.0058	1.0464	0.4722	1.5324
IEMM (𝑀=51,𝐿=3)	0.0046	1.7385	0.0067	1.0464	0.4782	1.5268
IEMM (𝑀=101,𝐿=3)	0.0015	1.7385	0.0071	1.0464	0.4788	1.5262
IEMM (𝑀=201,𝐿=3)	0.0017	1.7385	0.0073	1.0464	0.4791	1.5260
IEMM (𝑀=301,𝐿=3)	0.0017	1.7385	0.0073	1.0464	0.4791	1.5259
TM (𝑀=51,𝑁=30,𝐿=0)	0.0046	1.7385	0.0068	1.0464	0.4804	1.5248
TM (𝑀=101,𝑁=30,𝐿=0)	0.0015	1.7385	0.0074	1.0464	0.4820	1.5233
TM (𝑀=201,𝑁=30,𝐿=0)	0.0017	1.7385	0.0078	1.0464	0.4828	1.5224
TM (𝑀=301,𝑁=50,𝐿=0)	0.0017	1.7385	0.0080	1.0464	0.4831	1.5221
Evans and Linton [19]	0.0019	1.7385	0.0073	1.0464	0.4791	1.5259
Exact [1]	0.0018	1.7385	0.0073	1.0464	0.4792	1.5258