Explicit hybrid six–step, sixth order, fully symmetric methods for solving  y ″ = f (x, y). (25th March 2019)

• Record Type: Journal Article
• Authors: Fang, Jie; Liu, Chenglian; Hsu, Chieh‐Wen; Simos, Theodore E.; Tsitouras, Charalampos
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 9(2019)
• Page Start: 3305
• Page End: 3314
• Publication Date: 2019-03-25
• Subjects: constant coefficients -- initial value problem -- multistep -- phase lag; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5585
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A family of explicit, fully symmetric, sixth order, six‐step methods for the numerical solution of y ′′ = f ( x, y ) is studied. This family wastes two function evaluations per step and can be derived through interpolation techniques. An interval of periodicity is possessed and the phase lag is of high order. Numerical instabilities usually present in such type of multistep methods were circumvented. We conclude with extended numerical tests over a set of problems justifying our effort of dealing with the new methods.