An analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems
Reads0
Chats0
TLDR
In this paper, the authors derived stability and convergence results for the box and trapezoidal schemes applied to boundary value problems for linear singularly perturbed first order systems of o.d.Abstract:
Stability and convergence results are derived for the box and trapezoidal schemes applied to boundary value problems for linear singularly perturbed first order systems of o.d.e.'s without turning points.read more
Citations
More filters
Journal ArticleDOI
Asymptotic and numerical analysis of singular perturbation problems: A survey
Mohan K. Kadalbajoo,Y. N. Reddy +1 more
TL;DR: A brief survey of the asymptotic and numerical analysis of singular perturbation problems is given in this paper, with an eye toward the goal of developing general methods to solve such problems.
Journal ArticleDOI
Decoupling and Stability of Algorithms for Boundary Value Problems
TL;DR: In this paper, it was shown that the inherent initial value instability is an important prerequisite for a stable utilization of the decoupled representations from which the solutions are computed, and how this stability is related to the use of the boundary conditions.
Journal ArticleDOI
Uniform high-order difference schemes for a singularly perturbed two-point boundary value problem
TL;DR: The authors construit une famille de schemas aux differences finies uniformement precis pour le probleme du type −eu''+a(x)u'+b(x),u=f(x).
Journal ArticleDOI
Numerical methods for stiff two-point boundary value problems
TL;DR: In this article, the authors consider the two-point boundary value problem for stiff systems of ordinary differential equations and give robust difference approximations and present error estimates for these schemes and give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable to satisfy the correct smoothness conditions.
Journal ArticleDOI
Collocation for singular perturbation problems. II. Linear first order systems without turning points
Uri M. Ascher,R. Weiss +1 more
TL;DR: In this article, singularly perturbed linear boundary value problems for ODE's with variable coefficients were considered and convergence results were obtained for collocation schemes based on Gauss and Lobatto points.
References
More filters
Journal ArticleDOI
A collocation solver for mixed order systems of boundary value problems
TL;DR: Implementation of a spline collocation method for solving boundary value problems for mixed order systems of ordinary differential equations is discussed and the resulting general purpose code, COLSYS, is tested on a number of examples to demonstrate its stability, efficiency and flexibility.
Journal ArticleDOI
Difference approximations for singular perturbations of systems of ordinary differential equations
TL;DR: In this article, the authors consider difference methods for the solution of singular perturbations of boundary value problems and show that only approximations of low order accuracy can be used.
Book ChapterDOI
Numerical Methods for Singular Perturbation Problems
Barbro Kreiss,Heinz-Otto Kreiss +1 more
TL;DR: In this article, the two-point boundary value problem for a stiff system of ordinary differential equations is considered and an adaptive method to solve these problems even when turning points are present is discussed.
Journal ArticleDOI
Efficient Computer Manipulation of Tensor Products
TL;DR: It is shown how to construct a modified version sub i of a (presumably efficient) subroutine sub i for solving the linear system A sub i x = b, i=1,...,k, so that thelinear system can be solved by just one call to each of the subroutines SUB sub i .
Related Papers (5)
Collocation for Singular Perturbation Problems I: First Order Systems with Constant Coefficients
Uri M. Ascher,R. Weiss +1 more
Collocation for singular perturbation problems. II. Linear first order systems without turning points
Uri M. Ascher,R. Weiss +1 more