Trans maxima; A Maxima package for analytical solution of one dimensional linear system of transport equations

Yaprak R., Coşkun E.

3rd International Conference on Pure and Applied Mathematics ICPAM-VAN 2020, Van, Türkiye, 3 - 05 Eylül 2020, ss.111

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Van
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.111
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

    In this study we aim to develop a Maxima [1] package for analytical solution of linear system of one dimensional transport equations of the form

U_t + A_Ux = B_Uxx + CU + D (1)

where U = (u,v)  is the vector of unknowns, A, B and C are 2 × 2 constant matrices and D 2×1 is a constant vector. The package aims to solve the system over a finite interval with Dirichlet and Neumann boundary conditions, as well as Robin conditions with the aid of some numerical methods that may be needed for numerical computation of eigenvalues. The package aims to interactively asks for problem data (the coefficient matrices, initial and boundary conditions) and display both analytical solution and its graph if desired. Initial results for scalar transport equation will be illustrated.

    The motivation for the study came from a research work on wound healing model being studied by the authors.

MSC 2010: 35E05, 35E20, 35Q92, 35G35, 68U01

Keywords: Transport equation, analytic solution of partial differential equations, Maxima packages

References

[1] Maxima, a Computer Algebra System, URL: http://maxima.sourceforge.net/.

[2] E. Coskun, Maxima ile Sembolik Hesaplama ve Kodlama, URL: http://erhancoskun.com.tr, Trabzon, 2018.

[3] E. Coskun, Maxima Uygulamalarıyla Lineer Kısmi Diferansiyel Denklemlere Giris, URL: http://erhancoskun.com.tr