| Title:
|
On a high-order iterative scheme for a nonlinear Love equation (English) |
| Author:
|
Ngoc, Le Thi Phuong |
| Author:
|
Duy, Nguyen Tuan |
| Author:
|
Long, Nguyen Thanh |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
285-298 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L. T. P. Ngoc, N. T. Long (2011); L. X. Truong, L. T. P. Ngoc, N. T. Long (2009)) to get a convergent sequence at a rate of order $N \geq 2$ to a local unique weak solution of the above mentioned equation. (English) |
| Keyword:
|
nonlinear Love equation |
| Keyword:
|
Faedo-Galerkin method |
| Keyword:
|
convergence of order $N$ |
| MSC:
|
35L20 |
| MSC:
|
35L70 |
| idZBL:
|
Zbl 06486912 |
| idMR:
|
MR3419963 |
| DOI:
|
10.1007/s10492-015-0096-4 |
| . |
| Date available:
|
2015-05-15T07:39:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144264 |
| . |
| Reference:
|
[1] Albert, J.: On the decay of solutions of the generalized Benjamin-Bona-Mahony equation.J. Math. Anal. Appl. 141 (1989), 527-537. Zbl 0697.35116, MR 1009061, 10.1016/0022-247X(89)90195-9 |
| Reference:
|
[2] Amick, C. J., Bona, J. L., Schonbek, M. E.: Decay of solutions of some nonlinear wave equations.J. Differ. Equations 81 (1989), 1-49. Zbl 0689.35081, MR 1012198, 10.1016/0022-0396(89)90176-9 |
| Reference:
|
[3] Chattopadhyay, A., Gupta, S., Singh, A. K., Sahu, S. A.: Propagation of shear waves in an irregular magnetoelastic monoclinic layer sandwiched between two isotropic half-spaces.Internat. J. Engrg., Sci. Technol. 1 (2009), 228-244. |
| Reference:
|
[4] Clarkson, P. A.: New similarity reductions and Painlevé analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations.J. Phys. A, Math. Gen. 22 (1989), 3821-3848. Zbl 0711.35113, MR 1015235, 10.1088/0305-4470/22/18/020 |
| Reference:
|
[5] Deimling, K.: Nonlinear Functional Analysis.Springer Berlin (1985). Zbl 0559.47040, MR 0787404 |
| Reference:
|
[6] Dutta, S.: On the propagation of Love type waves in an infinite cylinder with rigidity and density varying linearly with the radial distance.Pure Applied Geophys. 98 (1972), 35-39. 10.1007/BF00875578 |
| Reference:
|
[7] Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities. Theory and Applications. Vol. I: Ordinary Differential Equations.Mathematics in Science and Engineering. Vol. 55 Academic Press, New York (1969). Zbl 0177.12403, MR 0379933 |
| Reference:
|
[8] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites nonlinéaires.French Etudes mathematiques Dunod; Gauthier-Villars, Paris (1969). MR 0259693 |
| Reference:
|
[9] Makhankov, V. G.: Dynamics of classical solitons (in nonintegrable systems).Phys. Rep. 35 (1978), 1-128. MR 0481361, 10.1016/0370-1573(78)90074-1 |
| Reference:
|
[10] Ngoc, L. T. P., Duy, N. T., Long, N. T.: A linear recursive scheme associated with the Love equation.Acta Math. Vietnam. 38 (2013), 551-562. Zbl 1310.35174, MR 3129917, 10.1007/s40306-013-0034-z |
| Reference:
|
[11] Ngoc, L. T. P., Duy, N. T., Long, N. T.: Existence and properties of solutions of a boundary problem for a Love's equation.Bull. Malays. Math. Sci. Soc. (2) 37 (2014), 997-1016. Zbl 1304.35231, MR 3295564 |
| Reference:
|
[12] Ngoc, L. T. P., Long, N. T.: A high order iterative scheme for a nonlinear Kirchhoff wave equation in the unit membrane.Int. J. Differ. Equ. 2011 (2011), Article ID 679528, 31 pages. Zbl 1242.35014, MR 2854955 |
| Reference:
|
[13] Ngoc, L. T. P., Truong, L. X., Long, N. T.: An $N$-order iterative scheme for a nonlinear Kirchhoff-Carrier wave equation associated with mixed homogeneous conditions.Acta Math. Vietnam. 35 (2010), 207-227. Zbl 1233.35134, MR 2731324 |
| Reference:
|
[14] Ogino, T., Takeda, S.: Computer simulation and analysis for the spherical and cylindrical ion-acoustic solitons.J. Phys. Soc. Jpn. 41 (1976), 257-264. 10.1143/JPSJ.41.257 |
| Reference:
|
[15] Parida, P. K., Gupta, D. K.: Recurrence relations for a Newton-like method in Banach spaces.J. Comput. Appl. Math. 206 (2007), 873-887. Zbl 1119.47063, MR 2333719, 10.1016/j.cam.2006.08.027 |
| Reference:
|
[16] Paul, M. K.: On propagation of Love-type waves on a spherical model with rigidity and density both varying exponentially with the radial distance.Pure Applied Geophys. 59 (1964), 33-37. Zbl 0135.23902, 10.1007/BF00880505 |
| Reference:
|
[17] Radochová, V.: Remark to the comparison of solution properties of Love's equation with those of wave equation.Apl. Mat. 23 (1978), 199-207. MR 0492985 |
| Reference:
|
[18] Seyler, C. E., Fenstermacher, D. L.: A symmetric regularized-long-wave equation.Phys. Fluids 27 (1984), 4-7. Zbl 0544.76170, 10.1063/1.864487 |
| Reference:
|
[19] Truong, L. X., Ngoc, L. T. P., Long, N. T.: High-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed homogeneous conditions.Nonlinear Anal., Theory Mathods Appl., Ser. A, Theory Methods 71 (2009), 467-484. Zbl 1173.35603, MR 2518053, 10.1016/j.na.2008.10.086 |
| Reference:
|
[20] Truong, L. X., Ngoc, L. T. P., Long, N. T.: The $N$-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed inhomogeneous conditions.Appl. Math. Comput. 215 (2009), 1908-1925. Zbl 1191.65122, MR 2557432, 10.1016/j.amc.2009.07.056 |
| . |
