Citas bibligráficas
Pulliti, Y., (2018). Implementación de un esquema de alto orden compacto para hallar la solución de la ecuación del calor bidimensional [Tesis, Pontificia Universidad Católica del Perú]. http://hdl.handle.net/20.500.12404/12591
Pulliti, Y., Implementación de un esquema de alto orden compacto para hallar la solución de la ecuación del calor bidimensional [Tesis]. PE: Pontificia Universidad Católica del Perú; 2018. http://hdl.handle.net/20.500.12404/12591
@mastersthesis{renati/19910,
title = "Implementación de un esquema de alto orden compacto para hallar la solución de la ecuación del calor bidimensional",
author = "Pulliti Carrasco, Yelinna Beatriz",
publisher = "Pontificia Universidad Católica del Perú",
year = "2018"
}
In the present work, that is based on [7] and [8], we analyze two methods to construct high order compact schemes to solve the bidimentional heat equation in a rectangular domain. Also we explain step by step the construction of a non efficient method and an eficient one (from the computational point of view) for calculating high order compact schemes. We start with the high order unidimensional schemes and end with the respective algorithm in pseudocode, this is for solving initial value problems with periodic boundary conditions for the bidimensional heat equation. Finally we study the general conditions for stability in the case of non periodic boundary conditions. This analysis is omitted by [7] and [8]. First we define h as the spatial discretizing step size, ¢t as the time discretizing step size, and N as the number of operations to make for finding the numerical solution. The first shown method is considered inefficient, on the other hand the second one is considered efficient according to the following criteria: A numerical scheme is considered efficient if if satisfy these three conditions: stability, accuracy order to the analytical solution superior to O(h2), and computational complexity inferior to O(N3) for the unidimensional case. Implicit schemes are prefered to explicit ones and asumming periodic boundary conditions, because it is difficult to find stable high order compact schemes with periodic and non periodic boundary conditions. Finally because of the computational complexity to find the analytical solution, it is preferred optimized algorithms to iterative altorithms with more than two nested loops. Finite difference methods imply vectorial and matricial operations, and this often increments the computational complexity of the implemented algorithms.
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