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BIT Numerical Mathematics

, Volume 28, Issue 4, pp 898–903 | Cite as

Efficient sixth order methods for nonlinear oscillation problems

  • R. M. Thomas
Part II Numerical Mathematics

Abstract

A class of two-step (hybrid) methods is considered for solving pure oscillation second order initial value problems. The nonlinear system, which results on applying methods of this type to a nonlinear differential system, may be solved using a modified Newton iteration scheme. From this class the author has derived methods which are fourth order accurate,P-stable, require only two (new) function evaluations per iteration and have a true real perfect square iteration matrix. Now, we propose an extension to sixth order,P-stable methods which require only three (new) function evaluations per iteration and for which the iteration matrix is a true realperfect cube. This implies that at most one real matrix must be factorised at each step. These methods have been implemented in a new variable step, local error controlling code.

Subject classification

AMS 65L05 

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References

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Copyright information

© BIT Foundations 1988

Authors and Affiliations

  • R. M. Thomas
    • 1
  1. 1.Department of MathematicsUMISTManchesterUnited Kingdom

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