Numerical Solution of Heat Equation with Singular Robin Boundary Condition

In this work we study the numerical solution of one-dimensional heat diffusion equation subject to Robin boundary conditions multiplied with a small parameter epsilon greater than zero. The numerical evidences tell us that the numerical solution of the differential equation with Robin boundary condition are very close in certain sense of the analytic solution of the problem with homogeneous Dirichlet boundary conditions when ε tends to zero.

Keywords:
Eigenvalue Problems; Finite Difference Method; Robin Boundary Conditions; Numerical Solutions

Authorship

G. LOZADA-CRUZ

Departamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista (Unesp), 15054-000, São José do Rio Preto, SP, Brazil. E-mail: german.lozada@sjrp.unesp.brUniversidade Estadual PaulistaBrazilSão José do Rio Preto, SP, BrazilDepartamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista (Unesp), 15054-000, São José do Rio Preto, SP, Brazil. E-mail: german.lozada@sjrp.unesp.br

C.E. RUBIO-MERCEDES

Programa de Matemática e Engenharia Física, Universidade Estadual do Mato Grosso do Sul (UEMS), Dourados, MS, Brazil. E-mail: cosme@uems.brUniversidade Estadual do Mato Grosso do SulBrazilDourados, MS, BrazilPrograma de Matemática e Engenharia Física, Universidade Estadual do Mato Grosso do Sul (UEMS), Dourados, MS, Brazil. E-mail: cosme@uems.br

J. RODRIGUES-RIBEIRO

Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (USP), São Carlos, SP, Brazil. E-mail:jrodrib@usp.brUniversidade de São PauloBrazilSão Carlos, SP, Brazil Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (USP), São Carlos, SP, Brazil. E-mail:jrodrib@usp.br

*Corresponding author: Cosme Eustaquio Rubio Mercedes - E-mail: cosme@uems.br

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (6)
Tables (2)
Formulas (36)

	0:0075	0:025	0:05	0:08
0	0:0012	0:0040	0:0076	0:0115
0:1000	0:0012	0:0039	0:0076	0:0114
0:2000	0:0012	0:0038	0:0076	0:0111
0:3000	0:0011	0:0036	0:0070	0:0105
0:4000	0:0010	0:0034	0:0065	0:0098
0:5000	0:0010	0:0031	0:0059	0:0088
0:6000	0:0009	0:0027	0:0052	0:0077
0:7000	0:0007	0:0023	0:0044	0:0064
0:8000	0:0006	0:0019	0:0034	0:0050
0:9000	0:0005	0:0014	0:0025	0:0034
1:0000	0:0003	0:0008	0:0014	0:0018

Simulation	ε	\|\|u _a - u _n \|\|
1	0.0075	0.00121
2	0.0250	0.00395
3	0.0500	0.00765
4	0.0800	0.01151

Brasil

Brasil

Numerical Solution of Heat Equation with Singular Robin Boundary Condition† † Work presented at the XXXVI National Congress of Applied and Computational Mathematics, Gramado, RS, Brazil, 2016.

ABSTRACT

Numerical Solution of Heat Equation with Singular Robin Boundary Condition^† † Work presented at the XXXVI National Congress of Applied and Computational Mathematics, Gramado, RS, Brazil, 2016.