Variable Mesh Spline Approximation Method for Solving Second Order Singularly Perturbed Turning Point Problems with Robin Boundary Conditions

2016 ◽  
Vol 3 (2) ◽  
pp. 891-903
Author(s):  
N. Geetha ◽  
A. Tamilselvan
Keyword(s):  
Boundary Conditions ◽  
Approximation Method ◽  
Turning Point ◽  
Spline Approximation ◽  
Second Order ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Variable Mesh ◽  
Robin Boundary

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

scholarly journals An iterative method for solving boundary value problems for second order differential equations

2016 ◽  
Vol 12 (8) ◽  
pp. 6489-6499
Author(s):  
Ymnah Salah Alruwaily
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Second Order ◽  
Robin Boundary Conditions ◽  
Second Order Differential Equations ◽  
Adomian Decomposition ◽  
Robin Boundary

The purpose of this paper is to investigate the application of the Adomian decomposition method (ADM) for solving boundary value problems for second-order differential equations with Robin boundary conditions. We first reformulate the boundary value problems for linear equations as a fixed point problems for a linear Fredholm integral operator, and then apply the ADM. We also extend our approach to include second-order nonlinear differential equations subject Robin boundary conditions.

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