Solving a nonlinear fractional Schrödinger equation using cubic B-splines

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Numerical solutions of Example 5.2 with \(\alpha =0.75\)

t	Exact solution		Numerical solution (CBSM)		Numerical solution (RBFM)
t	\(p_{1}(t)\)	\(p_{2}(t)\)	\(p^{*}_{1}(t)\)	\(p^{*}_{2}(t)\)	\(p^{*}_{1}(t)\)	\(p^{*}_{2}(t)\)
0.1	0.995004	0.099833	1.025001	0.127985	1.137524	0.124301
0.2	0.980067	0.198669	1.013504	0.224161	1.088189	0.143896
0.3	0.955336	0.295520	0.982968	0.320768	1.049366	0.279377
0.4	0.921061	0.389418	0.945771	0.417098	1.021368	0.361741
0.5	0.877583	0.479426	0.900361	0.508825	0.966005	0.448973
0.6	0.825336	0.564642	0.845493	0.595067	0.905687	0.534138
0.7	0.764842	0.644218	0.782633	0.675325	0.835528	0.610549
0.8	0.696707	0.717356	0.709399	0.749195	0.754661	0.681966
0.9	0.621609	0.783327	0.628863	0.817247	0.667961	0.746485
1	0.540302	0.841471	0.541769	0.878423	0.572605	0.803677
RMS			2.209 × 10⁻²	2.936 × 10⁻²	8.639 × 10⁻²	3.492 × 10⁻²
Execution time (second)			782.9		890.2