Stability analysis of the solution of the one-dimensional Richards equation by the finite difference method

2016 ◽  
Author(s):  
Héctor A. Pedrozo ◽  
Mario R. Rosenberger ◽  
Carlos E. Schvezov
1992 ◽  
Vol 26 (9-11) ◽  
pp. 2591-2594
Author(s):  
Y. S. Sin

A numerical method for the analysis of dispersion of pollutants in a one-dimensional rectangular estuary within a tidal cycle is presented. The finite-difference method is used to obtain a solution for the partial differential equation. An explicit scheme using multi-step procedure is adopted for solving the problem. It is shown that an analytical method is capable of predicting the dispersion of a slug load in the estuary as long as the effect due to the open boundary is negligible. However, the finite-difference method is required to study the dispersion effect of a continuous or variable pollutant source subjected to variable tidal velocity. The model developed is also applied in determining the effect of salinity intrusion within a tidal cycle due to different fresh water flows.


2019 ◽  
pp. 5-8

MÉTODO DE DIFERENCIAS FINITAS PARA UN PROBLEMA DE VALOR DE FRONTERA UNIDIMENSIONAL THE FINITE- DIFERENCE METHOD FOR A ONE-DIMENSIONAL BOUNDARY-VALUE PROBLEM Luis Jaime Collantes Santisteban, Samuel Collantes Santisteban DOI: https://doi.org/10.33017/RevECIPeru2006.0011/ RESUMEN En este trabajo se considera el problema de valor de frontera unidimensional dado en (1). Se aproxima la solución del problema mediante el método de diferencias finitas suponiendo que la función c(x) es no negativa sobre 0,1, lo que permite establecer la convergencia del método de aproximación. El uso del método de diferencias finitas, a la vez, involucra la solución de sistemas de ecuaciones lineales con matrices muy ralas, cuyos ceros están posicionados de una manera remarcable. Dichas matrices son de tipo tridiagonal. Para la solución de dichos sistemas se ha utilizado el método de Thomas. Palabras clave: problema de valor de frontera unidimensional, diferencias finitas, matriz tridiagonal, método de Thomas, momento flexionante. ABSTRACT In this work the one-dimensional boundary-value problem given in (1) is considered. The solution of the problem by means of finite-difference method comes near supposing that the function c(x) is nonnegative on 0,1, which allows to establish the convergence of the considered method of approximation. The use of the finite-difference method, in turn, involves the solution of linear systems with very sparse‟ matrices, whose zeros are arranged in quite remarkable fashion. These matrices are of tridiagonal type. For the solution of these systems the Thomas‟ method has been used. Keywords: one-dimensional boundary-value problem, finite-difference, tridiagonal matrix, Thomas‟ method, bending moment.


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