A parameter uniform difference scheme for the parameterized singularly perturbed problem with integral boundary condition

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Errors \(e_{ \lambda }^{ \varepsilon,N}\) computed ε-uniform errors \(e_{ \lambda }^{N}\) and convergence rates \(p_{ \lambda }^{ \varepsilon,N}\) on \(\omega_{N}\)

ε	N = 64	N = 128	N = 256	N = 512	N = 1024
2⁰	0.00749478	0.00402193	0.00204612	0. 00102448	0.00051242
2⁰	0.898	0.975	0.998	1.000
2⁻⁴	0.00742715	0.00399393	0.00203893	0.00102159	0.00051114
2⁻⁴	0.895	0.970	0.997	0.999
2⁻⁸	0.00723501	0.00391767	0.00202090	0.00101748	0.00051051
2⁻⁸	0.885	0.955	0.990	0.995
2⁻¹²	0.0070768	0.00385598	0.00200291	0.00102333	0.00051019
2⁻¹²	0.876	0.945	0.983	0.990
2⁻¹⁶	0.00692575	0.00379203	0.00198065	0.00100764	0.00050909
2⁻¹⁶	0.869	0.937	0.975	0.985
\(e_{\lambda }^{\varepsilon,N}\)	0.00749478	0.00402193	0.00204612	0. 00102448	0.00313856
\(p_{\lambda }^{\varepsilon,N}\)	0.898	0.975	0.998	1.000