| dc.contributor | LUIS HERNANDEZ MARTINEZ | |
| dc.contributor | HECTOR VAZQUEZ LEAL | |
| dc.creator | DELIA TORRES MUÑOZ | |
| dc.date | 2015-08 | |
| dc.date.accessioned | 2023-07-25T16:20:57Z | |
| dc.date.available | 2023-07-25T16:20:57Z | |
| dc.identifier | http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/131 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7805352 | |
| dc.description | The equations describing the behavior of a electronic circuit are nonlinear due to nonlinear
elements and the DC analysis is the first step for analyzing a nonlinear circuit and also to
find the solution, or solutions, of the system of equations. Methods like Newton Raphson
algorithm present disadvantages to solve nonlinear problems besides are not capable to
find multiple solutions. To overcome above problems the homotopy methods can locate
multiple solutions for a system of equations; however homotopy methods convergence
depends of the starting point, the continuous methods and nonlinearities. The homotopy
formulation require suitable path tracking techniques to accurately trace the homotopy
curve, the algorithm to path-tracking used in this work is the spherical algorithm because
it is geometrically clear and this characteristic can facilitate its programming. However
during programming hyperspheres method there were some problems as reversion of the
path on the curve and slow for tracing. In this thesis, two proposed methodologies are used
to solve the above problems, the first proposed methodology is based in calculating the
normal vector to the curve for detecting the problem of reversion then the methodology
is used to avoid the problem of reversion. The second methodology is achieved during the
tracing of the homotopy curve to reduce the number of iterations and the computational
time. Both strategies are implemented and programmed for the hyperspheres method;
also several case studies are solved, and we found satisfactory results for the path tracking
problem. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Instituto, Nacional de Astrofísica, Óptica y Electrónica | |
| dc.relation | citation:Torres-Muñoz D. | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | info:eu-repo/classification/Método Homotopy/Homotopy method | |
| dc.subject | info:eu-repo/classification/No lineal/Nonlinear | |
| dc.subject | info:eu-repo/classification/Ecuación no lineal/Equation nonlinear | |
| dc.subject | info:eu-repo/classification/Algoritmo de continuación/Continuation algorithm | |
| dc.subject | info:eu-repo/classification/cti/1 | |
| dc.subject | info:eu-repo/classification/cti/22 | |
| dc.subject | info:eu-repo/classification/cti/2203 | |
| dc.subject | info:eu-repo/classification/cti/2203 | |
| dc.title | Modified method of hyperspheres: tracing homotopic bounded paths in nonlinear circuits | |
| dc.type | info:eu-repo/semantics/doctoralThesis | |
| dc.audience | generalPublic | |
