A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition

2020 ◽  
Vol 63 (1-2) ◽  
pp. 813-828
Author(s):  
Devendra Kumar ◽  
Parvin Kumari
Keyword(s):  
Boundary Condition ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Collocation Scheme

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 A NUMERICAL STUDY ON THE DIFFERENCE SOLUTION OF SINGULARLY PERTURBED SEMILINEAR PROBLEM WITH INTEGRAL BOUNDARY CONDITION

2016 ◽  
Vol 21 (5) ◽  
pp. 644-658 ◽  
Author(s):  
Musa Cakir
Keyword(s):  
Boundary Condition ◽  
Numerical Solution ◽  
Numerical Study ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Uniform Mesh ◽  
Differential Problem ◽  
Difference Problem ◽  
Integral Boundary

The present study is concerned with the numerical solution, using finite difference method on a piecewise uniform mesh (Shishkin type mesh) for a singularly perturbed semilinear boundary value problem with integral boundary condition. First we discuss the nature of the continuous solution of singularly perturbed differential problem before presenting method for its numerical solution. The numerical method is constructed on piecewise uniform Shishkin type mesh. We show that the method is first-order convergent in the discrete maximum norm, independently of singular perturbation parameter except for a logarithmic factor. We give effective iterative algorithm for solving the nonlinear difference problem. Numerical results which support the given estimates are presented.

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