Solving inverse nodal problem with spectral parameter in boundary conditions

Figures & data

Figure 1. Approximate and exact solutions of inverse nodal problem using Chebyshev wavelet method in Example 4.1 with n=57: (***) for the exact solution and (- - -) for the approximate solution.

Table 1. Numerical values of nodes $x_j^n$ in Example 4.1 with n=13.

j	1	2	3	4	5	6
$x_j^n$	0.0423161315	0.1255556747	0.2088035859	0.2920431292	0.3752624706	0.4584616101
j	7	8	9	10	11	12
$x_j^n$	0.5416523818	0.6248515214	0.7080708628	0.7913104060	0.8745583172	0.9577978604

Table 2. Absolute error of exact and approximate solutions in Example 4.1.

	Absolute error $|q-\tilde{q}|$	Absolute error $|q-\tilde{q}|$
$t_i$	Chebyshev wavelet method	Chebyshev interpolation method
$0.041\overline{6}$	0.0808023978	0.0279601501
0.1250	0.0575215606	0.0064502819
$0.208\overline{3}$	0.1166642530	0.0012518098
$0.291\overline{6}$	0.1357508823	0.0004014580
0.3750	0.0811187572	0.0048876064
$0.458\overline{3}$	0.2147850235	0.0097981967
$0.541\overline{6}$	0.2225430976	0.0100129764
0.6250	0.1392119313	0.0060319169
$0.708\overline{3}$	0.3067156266	0.0010501754
$0.791\overline{6}$	0.3275786111	0.0004377981
0.8750	0.1679019186	0.0002027071
$0.958\overline{3}$	0.3771055756	0.0403948015