Adaptive Grids and High-Order Schemes for Solving Singular Perturbation Problems

2021 ◽  
Vol 14 (1) ◽  
pp. 69-82
Author(s):  
V. D. Liseikin ◽  
V. I. Paasonen
Keyword(s):  
Singular Perturbation ◽  
High Order ◽  
Singular Perturbation Problems ◽  
Adaptive Grids ◽  
High Order Schemes ◽  
Perturbation Problems

scholarly journals Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Essam R. El-Zahar
Keyword(s):  
Asymptotic Expansion ◽  
Singular Perturbation ◽  
Analytical Solutions ◽  
Source Term ◽  
High Order ◽  
Singular Perturbation Problems ◽  
Weakly Coupled System ◽  
Approximate Analytical Solutions ◽  
Discontinuous Source Term ◽  
Perturbation Problems

A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM). First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.

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