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
Keyword(s):  
Control Theory ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Numerical Approach ◽  
Singularly Perturbed

Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation

2019 ◽  
Vol 27 (5) ◽  
pp. 745-758 ◽  
Author(s):  
Dmitry V. Lukyanenko ◽  
Maxim A. Shishlenin ◽  
Vladimir T. Volkov
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Analysis ◽  
Boundary Value ◽  
Numerical Approach ◽  
Singularly Perturbed ◽  
Advection Equation ◽  
Unknown Boundary ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Time Periodic

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.

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.

Sign in / Sign up

Export Citation Format

Share Document