Theory of integral manifolds of singularly perturbed differential-difference equations

1983 ◽  
Vol 34 (6) ◽  
pp. 586-591 ◽  
Author(s):  
V. I. Fodchuk ◽  
I. M. Cherevko
Keyword(s):  
Difference Equations ◽  
Singularly Perturbed ◽  
Integral Manifolds

Efficient decomposition of singularly perturbed systems

2019 ◽  
Vol 14 (4) ◽  
pp. 410 ◽  
Author(s):  
Vladimir Sobolev
Keyword(s):  
Enzyme Kinetics ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Differential Systems ◽  
Integral Manifolds ◽  
Perturbed Systems ◽  
Method Of Integral Manifolds

The problem of the decomposition of singularly perturbed differential systems by the method of integral manifolds is studied and the application of the method to the problems of enzyme kinetics is considered.

Fitted Mesh Method for a Class of Singularly Perturbed Differential-Difference Equations

2015 ◽  
Vol 8 (4) ◽  
pp. 496-514 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Boundary Layer ◽  
Small Parameter ◽  
Uniform Convergence ◽  
Difference Equations ◽  
Numerical Study ◽  
Second Order ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Small Parameters ◽  
Spline Basis

AbstractThis paper deals with a more general class of singularly perturbed boundary value problem for a differential-difference equations with small shifts. In particular, the numerical study for the problems where second order derivative is multiplied by a small parameter ε and the shifts depend on the small parameter ε has been considered. The fitted-mesh technique is employed to generate a piecewise-uniform mesh, condensed in the neighborhood of the boundary layer. The cubic B-spline basis functions with fitted-mesh are considered in the procedure which yield a tridiagonal system which can be solved efficiently by using any well-known algorithm. The stability and parameter-uniform convergence analysis of the proposed method have been discussed. The method has been shown to have almost second-order parameter-uniform convergence. The effect of small parameters on the boundary layer has also been discussed. To demonstrate the performance of the proposed scheme, several numerical experiments have been carried out.

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