A class of collocation methods for numerical integration of initial value problems

Authors:
F. Costabile;A. Napoli
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
Cited 2

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The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
A family of implicit Chebyshev methods for the numerical integration of second- order differential equations

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Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The Chebyshev methods of Panovsky and Richardson as Runge-Kutta-Nystro¨m methods

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A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method

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Δh-Appell sequences and related interpolation problem

Numerical Algorithms

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Abstract

For the numerical solution of initial value problems a general procedure to determine global integration methods is derived and studied. They are collocation methods which can be easily implemented and provide a high order accuracy. They further provide globally continuous differentiable solutions. Computation of the integrals which appear in the coefficients are generated by a recurrence formula and no integrals are involved in the calculation. Numerical experiments provide favorable comparisons with other existing methods.