A SUM-DIFFERENCE METHOD FOR CONSTRUCTING AN ASYMPTOTIC SOLUTION TO A BOUNDARY VALUE PROBLEM OF A NONLINEAR DIFFERENCE EQUATION WITH A SMALL PARAMETER

2019 ◽  
Vol 19 (4) ◽  
pp. 255-259
Author(s):  
Asangul Alymbaev ◽  
Keyword(s):  
Finite Difference ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Asymptotic Solution ◽  
Small Parameter ◽  
Difference Equations ◽  
Difference Method ◽  
Financial Analysis ◽  
Boundary Value ◽  
Nonlinear Difference Equation

Finite-difference equations proved to be a convenient mathematical model on describing impulse systems, combinatorial analysis problems, discrete analogues of mathematical physics equations, financial analysis tasks, etc. Oneshould point out that difference equations are encountered in the numerical solution of various classes of differential and integro- differential ones using the finite difference method. The article deals with methods of constructing an asymptotic solution to the boundary value problem of a system of a nonlinear difference equation with a small parameter. The problem is solved by reducing the boundary-value problem to the Cauchy problem for a system of total-difference equations with a small parameter. The efficiency of the method algorithm for the asymptotic expansion of the task of a boundary value problem in a definite example is shown.

scholarly journals Boundary Value Problems for Fourth Order Nonlinearp-Laplacian Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qinqin Zhang
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Mountain Pass ◽  
Mountain Pass Lemma

We consider the boundary value problem for a fourth order nonlinearp-Laplacian difference equation containing both advance and retardation. By using Mountain pass lemma and some established inequalities, sufficient conditions of the existence of solutions of the boundary value problem are obtained. And an illustrative example is given in the last part of the paper.

scholarly journals MÉTODO DE DIFERENCIAS FINITAS PARA UN PROBLEMA DE VALOR DE FRONTERA UNIDIMENSIONAL

2019 ◽  
pp. 5-8
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problem ◽  
Difference Method ◽  
Sparse Matrices ◽  
Boundary Value ◽  
Bending Moment ◽  
One Dimensional ◽  
Dimensional Boundary ◽  
The One

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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