A finite difference method for a non-local boundary value problem for two-dimensional heat equation

2000 ◽  
Vol 112 (1) ◽  
pp. 133-142 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Difference Method ◽  
Boundary Value ◽  
Two Dimensional ◽  
Local Boundary ◽  
Non Local

A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation

2018 ◽  
Vol 26 (6) ◽  
pp. 835-857 ◽  
Author(s):  
Dinh Nho Hào ◽  
Le Thi Thu Giang ◽  
Sergey Kabanikhin ◽  
Maxim Shishlenin
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Weak Sense ◽  
Very Weak Solution ◽  
Local Boundary ◽  
The Cauchy Problem ◽  
Non Local

Abstract We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well-posed non-local boundary value problem whose solution is also understood in a very weak sense. A stable finite difference scheme is suggested for solving the non-local boundary value problem and then applied to stabilizing the Cauchy problem. Some numerical examples are presented for showing the efficiency of the method.

scholarly journals Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Singularly Perturbed ◽  
Local Boundary ◽  
Local Boundary Condition ◽  
Numerical Experimentation ◽  
Non Local ◽  
Delay Differential

Abstract In this paper, accelerated fitted finite difference method for solving singularly perturbed delay differential equation with non-local boundary condition is considered. To treat the non-local boundary condition, Simpson’s rule is applied. The stability and parameter uniform convergence for the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter ε and mesh size h. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and ε-uniformly convergent for h ≥ ε where the classical numerical methods fails to give good result, and it also improves the results of the methods existing in the literature.

scholarly journals A regularized method for two dimensional nonlinear heat equation backward in time

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 289-303 ◽  
Author(s):  
Huy Tuan ◽  
Duc Trong ◽  
Hoang Quan
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Nonlinear Heat Equation ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Local Boundary ◽  
Problem Method ◽  
Non Local ◽  
Regularized Method

In this paper, a non-local boundary value problem method for solving 2-D nonlinear heat equation backward in time is given. Some error estimates between the exact solution and its regularization approximation are provided and numerical examples show that the method works effectively.

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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