A NEW APPROACH FOR NUMERICAL SOLUTION OF LINEAR AND NON-LINEAR SYSTEMS


Creative Commons License

ZEYBEK H., DOLAPCİ İ. T.

JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, cilt.35, ss.165-180, 2017 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 35
  • Basım Tarihi: 2017
  • Doi Numarası: 10.14317/jami.2017.165
  • Dergi Adı: JOURNAL OF APPLIED MATHEMATICS & INFORMATICS
  • Sayfa Sayıları: ss.165-180

Özet

In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.