The Use of an lnvariance Condition in the Solution of Multiple-Scale Singular Perturbation Problems: Ordinary Differential Equations

1993 ◽  
Vol 90 (3) ◽  
pp. 225-248 ◽  
Author(s):  
S. L. Woodruff
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Ordinary Differential Equations ◽  
Multiple Scale ◽  
Singular Perturbation Problems ◽  
Perturbation Problems

Invariant manifolds in singular perturbation problems for ordinary differential equations

1990 ◽  
Vol 116 (1-2) ◽  
pp. 45-78 ◽  
Author(s):  
Kunimochi Sakamoto
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Ordinary Differential Equations ◽  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Singular Perturbation Problems ◽  
Manifold Theory ◽  
Perturbation Problems ◽  
Geometric Idea ◽  
Normally Hyperbolic Invariant Manifolds

SynopsisBased on Fenichel's geometric idea, invariant manifold theory is applied to singular perturbation problems. This approach clarifies the nature of outer and inner solutions. A specific condition is given to ensure the existence of heteroclinic connections between normally hyperbolic invariant manifolds. A method to approximate the connections is also presented.

scholarly journals HAAR WAVELET METHOD FOR SOLVING STIFF DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 14 (4) ◽  
pp. 467-481 ◽  
Author(s):  
Ülo Lepik
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Haar Wavelet ◽  
Singular Perturbation Problems ◽  
Stiff Differential Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Haar Wavelet Method ◽  
Perturbation Problems

Application of the Haar wavelet approach for solving stiff differential equations is discussed. Solution of singular perturbation problems is also considered. Efficiency of the recommended method is demonstrated by means of four numerical examples, mostly taken from well‐known textbooks.

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