IMPROVED LAGUERRE MATRIX METHOD FOR SOLVING SOME NONLINEAR FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Sezer M., Gürbüz B.

Advances in Mathematical Sciences and Applications, cilt.28, sa.1, ss.73-84, 2019 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 1
  • Basım Tarihi: 2019
  • Dergi Adı: Advances in Mathematical Sciences and Applications
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.73-84
  • Anahtar Kelimeler: Error estimations, Laguerre polynomials, Matrix and collocation methods, Nonlinear functional partial differential equations
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, a modified matrix-collocation method based on Laguerre polynomials to find the approximate solutions of the mentioned nonlinear functional differential equations under the initial or boundary conditions is proposed. These type equations are used as mathematical models in many problems in fields of engineering, mathematics, physics, chemistry, population dynamics, control theory and biology. There exists main challenges for solving the mentioned problems due to large range of variables, nonlinearity and multi-dimensionality, so on; thereby, the numerical methods have been developed by many authors. To show the effectiveness of this approach, some examples along with error estimations are illustrated by tables and figures; the consistency of the technique is analyzed.