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A one-step method for the numerical solution of ordinary non-linear second-order differential equations based upon lobatto four-point quadrature formula

Published online by Cambridge University Press:  09 April 2009

K. D. Sharma  and
R. G. Gupta
K. D. Sharma
Affiliation:
Computer Centre Indian Institute of Technology Hauz Khas, New Delhi-29, India
R. G. Gupta
Affiliation:
Department of Mathematics Indian Institute of Technology Hauz Khas, New Delhi-29, India
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Abstract

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This paper describes a one-step method besed upon the Lobatto four-point quadreture formula for the numerical integration of differential: y″(x) = f(x, y(x), y'(x)); y(x0)=y0, y'(x0)=y'0. The method has a local truncation error 0(h6) in y(x) and 0(h5) in y′(x). In the case of linear second-order differential equation, a stability criterion has been developed. Theoretical and computational comparisons of the new method existing method is discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 193 - 201
Copyright
Copyright © Australian Mathematical Society 1973

References

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