Adaptive Methods for the Direct Numerical Integrations of y”=ʃ(t,y,y’)

Rai, Sesappa A and Ananthakrishnaiah, U (1995) Adaptive Methods for the Direct Numerical Integrations of y”=ʃ(t,y,y’). Utilitas Mathematica , 47. pp. 129-135. ISSN 03153681

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Abstract

This paper deals with numerical methods involving higher order derivatives for the direct numerical integration of initial value problems of second order differential equations. The methods depend upon the parameters p and q which assume the values of the coefficients of y’ and y occurring in the given differential equation. The methods are unconditionally stable when applied to linear homogeneous second order differential equations with constant coefficients. Numerical results are presented for the bessels Van der Pol’s and general second oreder differential equations.

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