Article
| Title: | Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method (English) |
| Author: | Wang, Yu Ping |
| Author: | Akbarpoor Kiasary, Shahrbanoo |
| Author: | Yılmaz, Emrah |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 339-354 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples. (English) |
| Keyword: | Sturm-Liouville equation |
| Keyword: | inverse nodal problem |
| Keyword: | Frozen argument |
| Keyword: | nodal parameters |
| Keyword: | SCW method |
| MSC: | 34A55 |
| MSC: | 34B99 |
| MSC: | 34L40 |
| MSC: | 35Q60 |
| MSC: | 35R30 |
| DOI: | 10.21136/AM.2024.0038-21 |
| . | |
| Date available: | 2024-05-17T07:47:01Z |
| Last updated: | 2024-05-20 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152353 |
| . | |
| Reference: | [1] Akbarpoor, S., Koyunbakan, H., Dabbaghian, A.: Solving inverse nodal problem with spectral parameter in boundary conditions.Inverse Probl. Sci. Eng. 27 (2019), 1790-1801. Zbl 1461.34031, MR 4009877, 10.1080/17415977.2019.1597871 |
| Reference: | [2] Albeverio, S., Hryniv, R. O., Nizhnik, L. P.: Inverse spectral problems for non-local Sturm-Liouville operators.Inverse Probl. 23 (2007), 523-535. Zbl 1121.34014, MR 2309662, 10.1088/0266-5611/23/2/005 |
| Reference: | [3] Bondarenko, N. P., Buterin, S. A., Vasiliev, S. V.: An inverse spectral problem for Sturm-Liouville operators with frozen argument.J. Math. Anal. Appl. 472 (2019), 1028-1041. Zbl 1416.34015, MR 3906409, 10.1016/j.jmaa.2018.11.062 |
| Reference: | [4] Bondarenko, N. P., Yurko, V. A.: An inverse problem for Sturm-Liouville differential operators with deviating argument.Appl. Math. Lett. 83 (2018), 140-144. Zbl 1489.34105, MR 3795682, 10.1016/j.aml.2018.03.025 |
| Reference: | [5] Bondarenko, N. P., Yurko, V. A.: Partial inverse problems for the Sturm-Liouville equation with deviating argument.Math. Methods Appl. Sci. 41 (2018), 8350-8354. Zbl 1469.34034, MR 3891294, 10.1002/mma.5265 |
| Reference: | [6] Borg, G.: Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe: Bestimmung der Differentialgleichung durch die Eigenwerte.Acta Math. 78 (1946), 1-96 German. Zbl 0063.00523, MR 0015185, 10.1007/BF02421600 |
| Reference: | [7] Browne, P. J., Sleeman, B. D.: Inverse nodal problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions.Inverse Probl. 12 (1996), 377-381. Zbl 0860.34007, MR 1402097, 10.1088/0266-5611/12/4/002 |
| Reference: | [8] Buterin, S. A., Kuznetsova, M.: On the inverse problem for Sturm-Liouville-type operators with frozen argument: Rational case.Comput. Appl. Math. 39 (2020), Article ID 5, 15 pages. Zbl 1449.34265, MR 4036537, 10.1007/s40314-019-0972-8 |
| Reference: | [9] Buterin, S. A., Pikula, M., Yurko, V. A.: Sturm-Liouville differential operators with deviating argument.Tamkang J. Math. 48 (2017), 61-71. Zbl 1410.34230, MR 3623427, 10.5556/j.tkjm.48.2017.2264 |
| Reference: | [10] Buterin, S. A., Shieh, C.-T.: Incomplete inverse spectral and nodal problems for differential pencils.Result. Math. 62 (2012), 167-179. Zbl 1256.34010, MR 2964764, 10.1007/s00025-011-0137-6 |
| Reference: | [11] Buterin, S. A., Vasiliev, S. V.: On recovering a Sturm-Liouville-type operator with the frozen argument rationally proportioned to the interval length.J. Inverse Ill-Posed Probl. 27 (2019), 429-438. Zbl 1422.34214, MR 3962691, 10.1515/jiip-2018-0047 |
| Reference: | [12] Buterin, S. A., Yurko, V. A.: An inverse spectral problem for Sturm-Liouville operators with a large constant delay.Anal. Math. Phys. 9 (2019), 17-27. Zbl 1423.34087, MR 3933524, 10.1007/s13324-017-0176-6 |
| Reference: | [13] Chen, X., Cheng, Y. H., Law, C. K.: Reconstructing potentials from zeros of one eigenfunction.Trans. Am. Math. Soc. 363 (2011), 4831-4851. Zbl 1232.34021, MR 2806693, 10.1090/S0002-9947-2011-05258-X |
| Reference: | [14] Cheng, Y.-H., Law, C. K., Tsay, J.: Remarks on a new inverse nodal problem.J. Math. Anal. Appl. 248 (2000), 145-155. Zbl 0960.34018, MR 1772587, 10.1006/jmaa.2000.6878 |
| Reference: | [15] Gulsen, T., Yilmaz, E., Akbarpoor, S.: Numerical investigation of the inverse nodal problem by Chebyshev interpolation method.Thermal Sci. 22 (2018), S123--S136. 10.2298/TSCI170612278G |
| Reference: | [16] Guo, Y., Wei, G.: Inverse problems: Dense nodal subset on an interior subinterval.J. Differ. Equations 255 (2013), 2002-2017. Zbl 1288.34013, MR 3072679, 10.1016/j.jde.2013.06.006 |
| Reference: | [17] Hald, O. H., McLaughlin, J. R.: Solutions of inverse nodal problems.Inverse Probl. 5 (1989), 307-347. Zbl 0667.34020, MR 0999065, 10.1088/0266-5611/5/3/008 |
| Reference: | [18] Hu, Y.-T., Bondarenko, N. P., Yang, C.-F.: Traces and inverse nodal problem for Sturm-Liouville operators with frozen argument.Appl. Math. Lett. 102 (2020), Article ID 106096, 7 pages. Zbl 1444.34076, MR 4024736, 10.1016/j.aml.2019.106096 |
| Reference: | [19] Krall, A. M.: The development of general differential and general differential-boundary systems.Rocky Mt. J. Math. 5 (1975), 493-542. Zbl 0322.34009, MR 0409946, 10.1216/RMJ-1975-5-4-493 |
| Reference: | [20] Kuryshova, Y. V.: Inverse spectral problem for integro-differential operators.Math. Notes 81 (2007), 767-777. Zbl 1142.45006, MR 2349102, 10.1134/S0001434607050240 |
| Reference: | [21] Law, C. K., Shen, C.-L., Yang, C.-F.: The inverse nodal problem on the smoothness of the potential function.Inverse Probl. 15 (1999), 253-263. Zbl 0921.34028, MR 1675348, 10.1088/0266-5611/15/1/024 |
| Reference: | [22] Law, C. K., Yang, C.-F.: Reconstructing the potential function and its derivatives using nodal data.Inverse Probl. 14 (1998), 299-312. Zbl 0901.34023, MR 1619374, 10.1088/0266-5611/14/2/006 |
| Reference: | [23] McLaughlin, J. R.: Inverse spectral theory using nodal points as data: A uniqueness result.J. Differ. Equations 73 (1988), 342-362. Zbl 0652.34029, MR 0943946, 10.1016/0022-0396(88)90111-8 |
| Reference: | [24] Neamaty, A., Akbarpoor, S.: Numerical solution of inverse nodal problem with an eigenvalue in the boundary condition.Inverse Probl. Sci. Eng. 25 (2017), 978-994. Zbl 1371.65066, MR 3635003, 10.1080/17415977.2016.1209751 |
| Reference: | [25] Nizhnik, L.: Inverse nonlocal Sturm-Liouville problem.Inverse Probl. 26 (2010), Article ID 125006, 9 pages. Zbl 1217.34040, MR 2737740, 10.1088/0266-5611/26/12/125006 |
| Reference: | [26] Pikula, M.: Determination of a differential operator of Sturm-Liouville type with retarded argument by two spectra.Mat. Vesn. 43 (1991), 159-171 Russian. Zbl 0776.34009, MR 1202169 |
| Reference: | [27] Pöschel, J., Trubowitz, E.: Inverse Spectral Theory.Pure and Applied Mathematics 130. Academic Press, Boston (1987). Zbl 0623.34001, MR 0894477, 10.1016/s0079-8169(08)x6138-0 |
| Reference: | [28] Rundell, W., Sacks, P. E.: The reconstruction of Sturm-Liouville operators.Inverse Probl. 8 (1992), 457-482. Zbl 0762.34003, MR 1166492, 10.1088/0266-5611/8/3/007 |
| Reference: | [29] Shieh, C.-T., Yurko, V. A.: Inverse nodal and inverse spectral problems for discontinuous boundary value problems.J. Math. Anal. Appl. 347 (2008), 266-272. Zbl 1209.34014, MR 2433842, 10.1016/j.jmaa.2008.05.097 |
| Reference: | [30] Vladičić, V., Pikula, M.: An inverse problem for Sturm-Liouville-type differential equation with a constant delay.Sarajevo J. Math. 12 (2016), 83-88. Zbl 1424.34264, MR 3511149, 10.5644/SJM.12.1.06 |
| Reference: | [31] Wang, Y. P., Lien, K. Y., Shieh, C.-T.: Inverse problems for the boundary value problem with the interior nodal subsets.Appl. Anal. 96 (2017), 1229-1239. Zbl 1410.34064, MR 3627617, 10.1080/00036811.2016.1183770 |
| Reference: | [32] Wang, Y. P., Shieh, C.-T., Miao, H. Y.: Reconstruction for Sturm-Liouville equations with a constant delay with twin-dense nodal subsets.Inverse Probl. Sci. Eng. 27 (2019), 608-617. Zbl 1461.34036, MR 3918035, 10.1080/17415977.2018.1489803 |
| Reference: | [33] Wang, Y. P., Yurko, V. A.: On the inverse nodal problems for discontinuous Sturm-Liouville operators.J. Differ. Equations 260 (2016), 4086-4109. Zbl 1342.34028, MR 3437580, 10.1016/j.jde.2015.11.004 |
| Reference: | [34] Wang, Y. P., Zhang, M., Zhao, W., Wei, X.: Reconstruction for Sturm-Liouville operators with frozen argument for irrational cases.Appl. Math. Lett. 111 (2021), Article ID 106590, 6 pages. Zbl 1524.34183, MR 4119344, 10.1016/j.aml.2020.106590 |
| Reference: | [35] Wang, Y., Zhu, L.: SCW method for solving the fractional integro-differential equations with a weakly singular kernel.Appl. Math. Comput. 275 (2016), 72-80. Zbl 1410.65288, MR 3437690, 10.1016/j.amc.2015.11.057 |
| Reference: | [36] Wei, X., Miao, H., Ge, C., Zhao, C.: An inverse problem for Sturm-Liouville operators with nodal data on arbitrarily-half intervals.Inverse Probl. Sci. Eng. 29 (2021), 305-317. Zbl 1470.65134, MR 4226240, 10.1080/17415977.2020.1779711 |
| Reference: | [37] Yang, C.-F., Yang, X.-P.: Inverse nodal problems for the Sturm-Liouville equation with polynomially dependent on the eigenparameter.Inverse Probl. Sci. Eng. 19 (2011), 951-961. Zbl 1248.34013, MR 2836942, 10.1080/17415977.2011.565874 |
| Reference: | [38] Yang, X.-F.: A new inverse nodal problem.J. Differ. Equations 169 (2001), 633-653. Zbl 0977.34021, MR 1808480, 10.1006/jdeq.2000.3911 |
| Reference: | [39] lmaz, E. Yı, Koyunbakan, H.: Reconstruction of potential function and its derivatives for Sturm-Liouville problem with eigenvalues in boundary condition.Inverse Probl. Sci. Eng. 18 (2010), 935-944. Zbl 1205.65215, MR 2743231, 10.1080/17415977.2010.492514 |
| Reference: | [40] Yurko, V. A.: An inverse spectral problem for integro-differential operators.Far East J. Math. Sci. (FJMS) 92 (2014), 247-261. Zbl 1328.47051, MR 3535366 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
