| Title:
|
Semi-analytical approach to initial problems for systems of nonlinear partial differential equations with constant delay (English) |
| Author:
|
Šamajová, Helena |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
163-172 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with the differential transform method for solving of an initial value problem for a system of two nonlinear functional partial differential equations of parabolic type. We consider non-delayed as well as delayed types of coupling and the different variety of initial functions are thought over. The convergence of solutions and the error estimation to the presented procedure is studied. Two numerical examples for non-delayed and delayed systems are included. (English) |
| Keyword:
|
Nonlinear partial differential equation, parabolic type equation, delayed equation, system of partial differential equation, initial problem |
| MSC:
|
35K51 |
| MSC:
|
35K55 |
| MSC:
|
35K61 |
| . |
| Date available:
|
2019-09-27T07:52:14Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703053 |
| . |
| Reference:
|
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| Reference:
|
[2] Khan, Y., Svoboda, Z., Šmarda, Z.: Solving certain classes of Lane-Emden type equations using the differential transformation method., Advances in Difference Equations, 174, (2012). MR 3016691 |
| Reference:
|
[3] Odibat, Z. M., Bertelle, C., Aziz-Alaouic, M. A., Duchampd, H. E. G.: A multi-step differential transform method and application to non-chaotic or chaotic systems., Computers and Mathematics with Applications, 59, (2010), pp. 1462-1472. MR 2591936, 10.1016/j.camwa.2009.11.005 |
| Reference:
|
[4] Odibat, Z. M., Kumar, S., Shawagfeh, N., Alsaedi, A., Hayat, T.: A study on the convergence conditions of generalized differential transform method., Mathematical Methods in the Applied Sciences, 40, (2017), pp 40-48. MR 3583033, 10.1002/mma.3961 |
| Reference:
|
[5] Polyanin, A. D., Zhurov, A. I.: Functional constraints method for constructing exact solutions to delay reactiondiffusion equations and more complex nonlinear equations., Commun. Nonlinear Sci. Numer. Simulat., 19, (2014), pp 417-430. MR 3111621, 10.1016/j.cnsns.2013.07.017 |
| Reference:
|
[6] Rebenda, J., Šmarda, Z.: A differential transformation approach for solving functional differential equations with multiple delays., Commun. Nonlinear Sci. Numer. Simulat., 48, (2017), pp. 246-257. MR 3607372, 10.1016/j.cnsns.2016.12.027 |
| Reference:
|
[7] Rebenda, J., Šmarda, Z., Khan, Y.: A New Semi-analytical Approach for Numerical Solving of Cauchy Problem for Differential Equations with Delay., FILOMAT, 31, (2017), pp. 4725-4733. MR 3725533, 10.2298/FIL1715725R |
| . |
