High Order Finite Difference Schemes for the Solution of Second Order Initial Value Problems

Pierluigi Amodio2, Giuseppina Settanni3
Dipartimento di Matematica,
Universit`a di Bari,
I-70125 Bari, Italy
Received 22 February, 2010; accepted in revised form 13 April, 2010
Abstract: The numerical solution of second order ordinary differential equations with initial
conditions is here approached by approximating each derivative by means of a set of finite
difference schemes of high order. The stability properties of the obtained methods are
discussed. Some numerical tests, reported to emphasize pros and cons of the approach,
motivate possible choices on the use of these formulae.

c 2010 European Society of Computational Methods in Sciences and Engineering
Keywords: Second order Initial Value Problems, finite difference schemes, Boundary Value
Methods, absolute stability.

 

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