Discrete approximation for a two-parameter singularly perturbed boundary value problem having discontinuity in convection coefficient and source term

2019 ◽  
Vol 359 ◽  
pp. 102-118 ◽  
Author(s):  
T. Prabha ◽  
M. Chandru ◽  
V. Shanthi ◽  
H. Ramos
Keyword(s):  
Boundary Value Problem ◽  
Source Term ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Discrete Approximation ◽  
Convection Coefficient ◽  
Two Parameter

scholarly journals Numerical Solution of Singularly Perturbed Two Parameter Problems using Exponential Splines

2021 ◽  
Vol 26 (2) ◽  
pp. 160-172
Author(s):  
P. Padmaja ◽  
P. Aparna ◽  
Rama Subba Reddy Gorla ◽  
N. Pothanna
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Shishkin Mesh ◽  
Numerical Results ◽  
Singularly Perturbed ◽  
Perturbation Parameters ◽  
Two Parameter

Abstract In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The boundary value problem is solved on a Shishkin mesh by using exponential splines. Numerical results are tabulated for different values of the perturbation parameters. From the numerical results, it is found that the method approximates the exact solution very well.

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

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