Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 2, 45 - 48, 30.11.2019
https://doi.org/10.34088/kojose.635255

Öz

Kaynakça

  • Paweletz N., Knierim M., 1989. Tumor-related angiogenesis. Critical Reviews in Oncology, 9(3), 197-242.
  • Levine H. A., Sleeman B. D., 2000. A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Mathematical Biosciences, 168, 77-115.
  • Pamuk S., Gürbüz A., 2004. Stability analysis of the steady-state solution of a mathematical model in tumor angiogenesis. Global Analysis and Applied Mathematics, 729, 369-373.
  • Pamuk S., 2003. Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis. Mathematical Models and Methods in Applied Sciences, 13(1), 19-33.
  • Pamuk S., 2004. Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source. Mathematical Biosciences, 189, 21-38
  • Bender C.M., Orszag S.A., 1999. Advanced Mathematical Methods for Scientists and Engineers, Springer, New York.
  • Hunter J.K., 2004. Asymptotic Analysis and Singular Perturbation Theory, University of California at Davis, California.
  • Rice R. G., Do D. D., 1995. Applied Mathematics And Modeling For Chemical Engineers, John Wiley and Sons Inc., New York.

Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis

Yıl 2019, Cilt: 2 Sayı: 2, 45 - 48, 30.11.2019
https://doi.org/10.34088/kojose.635255

Öz

In
this work, we obtain the regular perturbation solutions of a mathematical model
in tumor angiogenesis in one and two space dimensions. Our results show that
the solutions we have obtained are in good agreement with the solutions
obtained by other methods. We also present our results in Matlab generated
figures.

Kaynakça

  • Paweletz N., Knierim M., 1989. Tumor-related angiogenesis. Critical Reviews in Oncology, 9(3), 197-242.
  • Levine H. A., Sleeman B. D., 2000. A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Mathematical Biosciences, 168, 77-115.
  • Pamuk S., Gürbüz A., 2004. Stability analysis of the steady-state solution of a mathematical model in tumor angiogenesis. Global Analysis and Applied Mathematics, 729, 369-373.
  • Pamuk S., 2003. Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis. Mathematical Models and Methods in Applied Sciences, 13(1), 19-33.
  • Pamuk S., 2004. Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source. Mathematical Biosciences, 189, 21-38
  • Bender C.M., Orszag S.A., 1999. Advanced Mathematical Methods for Scientists and Engineers, Springer, New York.
  • Hunter J.K., 2004. Asymptotic Analysis and Singular Perturbation Theory, University of California at Davis, California.
  • Rice R. G., Do D. D., 1995. Applied Mathematics And Modeling For Chemical Engineers, John Wiley and Sons Inc., New York.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yazılım Mühendisliği (Diğer)
Bölüm Makaleler
Yazarlar

Melike Keleş Bu kişi benim 0000-0002-7457-5873

Serdal Pamuk 0000-0002-0934-9976

Yayımlanma Tarihi 30 Kasım 2019
Kabul Tarihi 27 Kasım 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 2

Kaynak Göster

APA Keleş, M., & Pamuk, S. (2019). Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis. Kocaeli Journal of Science and Engineering, 2(2), 45-48. https://doi.org/10.34088/kojose.635255