A Boundary Value Problem for a Singularly Perturbed Differential Equation

1998 ◽  
pp. 384-395
Author(s):  
N. Levinson
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Singularly Perturbed Differential Equation ◽  
Perturbed Differential Equation

scholarly journals Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 213 ◽  
Author(s):  
Assiya Zhumanazarova ◽  
Young Im Cho
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Singularly Perturbed Problems ◽  
Cauchy Function ◽  
Higher Derivatives ◽  
Singularly Perturbed Differential Equation ◽  
Perturbed Differential Equation

In this study, the asymptotic behavior of the solutions to a boundary value problem for a third-order linear integro-differential equation with a small parameter at the two higher derivatives has been examined, under the condition that the roots of the additional characteristic equation are negative. Via the scheme of methods and algorithms pertaining to the qualitative study of singularly perturbed problems with initial jumps, a fundamental system of solutions, the Cauchy function, and the boundary functions of a homogeneous singularly perturbed differential equation are constructed. Analytical formulae for the solutions and asymptotic estimates of the singularly perturbed problem are obtained. Furthermore, a modified degenerate boundary value problem has been constructed, and it was stated that the solution of the original singularly perturbed boundary value problem tends to this modified problem’s solution.

Sign in / Sign up

Export Citation Format

Share Document