A Robust Numerical Approach for Singularly Perturbed Third Order Boundary Value Problem on Layer Adapted Meshes

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
S. R. Sahu ◽  
J. Mohapatra ◽  
L. Govindrao
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Numerical Approach ◽  
Singularly Perturbed ◽  
Third Order

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.

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