Table 3 Relative output error and output error estimator effectivity for system 1 for parameter values L ^x =1 , L ^z =1.1 and E _i =1 , 1≤i≤I

$\frac{s^h\left(\mu \right)-{\tilde{s}}^{\mathrm{PR}}\left(\mu \right)}{{\tilde{s}}^{\mathrm{PR}}\left(\mu \right)}$

4.67978e-4

2.31664e-4

2.5646e-5

$\frac{{\mathrm{\Delta }}^{s;0}\left(\mu \right)}{s^h\left(\mu \right)-{\tilde{s}}^{\mathrm{PR}}\left(\mu \right)}$

28.3

14.8

67.6