1. Trigonometric fitted, eighth‐order explicit Numerov‐type methods.
- Author
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Berg, Dmitry B., Simos, T. E., and Tsitouras, Ch.
- Subjects
- *
INITIAL value problems , *TRIGONOMETRIC functions , *SET theory , *COEFFICIENTS (Statistics) , *COMPARATIVE studies - Abstract
We consider the integration of the special second‐order initial value problem of the form y ′′ = f ( x , y ). A recently introduced family of 7 stages, eighth‐order methods, sharing constant coefficients, is used as base. This family is properly modified to derive phase fitted and zero dissipative methods (ie, trigonometric fitted) that are best suited for integrating oscillatory problems. Numerical tests over a set of problems shows enhanced performance when the purely linear part of the problems is rather large in comparison with the rest of nonlinear parts. An appendix implementing a MATLAB listing with the coefficients of the new method is also given. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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