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 A New Numerical Algorithm for Two-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Lihua Guo ◽  
Boying Wu ◽  
Dazhi Zhang
Keyword(s):  
Exact Solution ◽  
Error Analysis ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Algorithm ◽  
Numerical Stability ◽  
Boundary Value ◽  
Numerical Results ◽  
Point Boundary ◽  
Stability And Error Analysis

We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that then-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

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