Uniformly convergent extended cubic B-spline collocation method for two parameters singularly perturbed time-delayed convection-diffusion problems

Table 2 \(E_{\varepsilon ,\mu }^{N,M}\) and \(p^{N,M}_{\varepsilon ,\mu }\) with \(\mu =10^{-4}, \lambda =-1e-03,\) for Example 1

\(\varepsilon \downarrow \)	\( N=32\)	\( N=64 \)	\( N=128 \)	\( N=256 \)
\(\varepsilon \downarrow \)	\( \Delta t=0.25/2\)	\( \Delta t=0.25/2^{2}\)	\( \Delta t=0.25/2^{3} \)	\( \Delta t=0.25/2^{4} \)
\(10^{-0}\)	\( 5.7908e-03 \)	\( 3.6490e-03 \)	\( 2.1309e-03 \)	\( 1.1633e-03 \)
\(10^{-0}\)	0.66626	0.77604	0.87324	\( 1.1633e-03 \)
\(10^{-2}\)	\( 1.0523e-02 \)	\( 5.4742e-03 \)	\( 2.7938e-03 \)	\( 1.4116e-03 \)
\(10^{-2}\)	0.94283	0.97042	0.98490	\( 1.4116e-03 \)
\(10^{-4}\)	\( 1.0658e-02 \)	\( 5.5311e-03 \)	\( 2.8188e-03 \)	\( 1.4230e-03 \)
\(10^{-4}\)	0.94630	0.97249	0.98615	\( 1.4230e-03 \)
\(10^{-6}\)	\( 1.0662e-02 \)	\( 5.5324e-03 \)	\( 2.8191e-03 \)	\( 1.4231e-03 \)
\(10^{-6}\)	0.94650	0.97267	0.98620	\( 1.4231e-03 \)
\(10^{-8}\)	\( 1.0663e-02 \)	\( 5.5336e-03 \)	\( 2.8200e-03 \)	\( 1.4237e-03 \)
\(10^{-8}\)	0.94632	0.97252	0.98605	\( 1.4237e-03 \)
\(10^{-10}\)	\( 1.0663e-02 \)	\( 5.5336e-03 \)	\( 2.8200e-03 \)	\( 1.4237e-03 \)
\(10^{-10}\)	0.94632	0.97252	0.98605	\( 1.4237e-03 \)
\(10^{-12}\)	\( 1.0663e-02 \)	\( 5.5336e-03 \)	\( 2.8200e-03 \)	\( 1.4237e-03 \)
\(10^{-12}\)	0.94632	0.97252	0.98605	\( 1.4237e-03 \)
\(E_{\varepsilon ,\mu }^{N,M}\)	\( 1.0663e-02 \)	\( 5.5336e-03 \)	\( 2.8200e-03 \)	\( 1.4880e-03 \)
\(p_{\varepsilon ,\mu }^{N,M}\)	0.94632	0.97252	0.92232	-

ISSN: 1756-0500