Power Series Solutions of a NODE Systemin the Complex Domain
| dc.contributor.author | Madiyeva, Aigerim | |
| dc.date.accessioned | 2018-05-28T09:00:04Z | |
| dc.date.available | 2018-05-28T09:00:04Z | |
| dc.date.issued | 2018-05-10 | |
| dc.description.abstract | In this Capstone Project, we analyze a second order nonlinear ordinary differential equation (NODE), y^" (x)=f(y^',y) that is impossible to solve analytically. First, using the Taylor Power Series method, we obtain a series expansion of the solution y(x) about x = 0 for x ∈R and find that this series diverges for values of x a little above x = 1. This implies that the equation has a singularity in the complex domain. Therefore, we investigate this NODE by using Laurent expansions about the unknown singularity at x =x_*, which is called movable because its location depends on the initial conditions. By finding the general form of these expansions, we obtain approximate expressions for the singularity closest to x = 0 and thus are able to estimate the radius of convergence for different initial conditions. We also integrate numerically the solutions in the real x, y plane and demonstrate the connection of the global form of the solutions of the problem with the predictions of our laurent series expansions in the complex x- plane. | en_US |
| dc.identifier.citation | Madiyeva, Aigerim. (2018) Power Series Solutions of a NODE Systemin the Complex Domain. Nazarbayev University School of Science and Technology | en_US |
| dc.identifier.uri | http://nur.nu.edu.kz/handle/123456789/3201 | |
| dc.language.iso | en | en_US |
| dc.publisher | Nazarbayev University School of Science and Technology | |
| dc.rights | Attribution-NonCommercial-ShareAlike 3.0 United States | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/us/ | * |
| dc.subject | complex domain | en_US |
| dc.subject | Nonlinear ordinary differential equations | en_US |
| dc.title | Power Series Solutions of a NODE Systemin the Complex Domain | en_US |
| dc.type | Capstone Project | en_US |
| workflow.import.source | science |