A New Method for Elliptic Partial Differential Equations

Baykuş Savaşaneril N.

7 th International Students Science Congress, İzmir, Türkiye, 12 - 13 Mayıs 2023, ss.141-150

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: İzmir
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.141-150
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

The study proposes a matrix method based on collocation points and Taylor polynomials for approximating the solution of elliptic partial differential equations. This method reduces the problem to solving a matrix equation with unknown Taylor coefficients, which are determined using the collocation points. The solution is then expressed in terms of Taylor polynomials. The technique is illustrated using a descriptive example, and the results are compared with a table and figure. The numerical calculations are performed using a program written in WOLFRAM MATHEMATICA 13.0.

Keywords: partial differential equations, Taylor polynomials, boundary value problems, matrix - collocation method.