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Enright, W. H.

Continuous numerical methods for ODEs with defect control. (English) Zbl 0982.65078

J. Comput. Appl. Math. 125, No. 1-2, 159-170 (2000).
In general-purpose numerical methods for ordinary differential equations (ODEs) generating continuous piecewise polynomial approximations the order of accuracy can naturally be controlled by means of defect control mechanisms. The paper reviews the advantages of these methods and presents applications to initial- and boundary-value problems. Applications to delay differential equations and differential algebraic equations are also discussed.
Reviewer: Thomas Sonar (Braunschweig)

Cited in 20 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34B15 Nonlinear boundary value problems for ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L80 Numerical methods for differential-algebraic equations
34K25 Asymptotic theory of functional-differential equations

Keywords:

continuous piecewise polynomial approximations; defect control; delay differential equations; differential algebraic equations

Software:

STDTST; NSDTST
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\textit{W. H. Enright}, J. Comput. Appl. Math. 125, No. 1--2, 159--170 (2000; Zbl 0982.65078)
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References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.