A Numerical Approach for Solving Nonlinear Singularly Perturbed Boundary Value Problem Arising in Control Theory

2021 ◽  
Vol 10 (1) ◽  
pp. 151-159
Author(s):  
P. Murali Mohan Kumar ◽  
A. S. V. Ravi Kanth
2019 ◽  
Vol 27 (5) ◽  
pp. 745-758 ◽  
Author(s):  
Dmitry V. Lukyanenko ◽  
Maxim A. Shishlenin ◽  
Vladimir T. Volkov

Abstract In this paper, a new asymptotic-numerical approach to solving an inverse boundary value problem for a nonlinear singularly perturbed parabolic equation with time-periodic coefficients is proposed. An unknown boundary condition is reconstructed by using known additional information about the location of a moving front. An asymptotic analysis of the direct problem allows us to reduce the original inverse problem to that with a simpler numerical solution. Numerical examples demonstrate the efficiency of the method.


Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova

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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