A uniformly convergent numerical scheme for singularly perturbed differential equation with integral boundary condition arising in neural network

2019 ◽  
Vol 10 (4) ◽  
pp. 340
Author(s):  
D. Shakti ◽  
J. Mohapatra
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Boundary Condition ◽  
Numerical Scheme ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Uniformly Convergent ◽  
Singularly Perturbed Differential Equation ◽  
Perturbed Differential Equation

scholarly journals Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Numerical Integration ◽  
Operator Method ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Singularly Perturbed Problems ◽  
Integral Boundary ◽  
Uniformly Convergent ◽  
Exponentially Fitted ◽  
Fitted Operator

In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent.

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