Research Article

Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis

Volume: 2 Number: 2 November 30, 2019
EN

Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis

Abstract

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.

Keywords

References

  1. Paweletz N., Knierim M., 1989. Tumor-related angiogenesis. Critical Reviews in Oncology, 9(3), 197-242.
  2. 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.
  3. 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.
  4. 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.
  5. 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
  6. Bender C.M., Orszag S.A., 1999. Advanced Mathematical Methods for Scientists and Engineers, Springer, New York.
  7. Hunter J.K., 2004. Asymptotic Analysis and Singular Perturbation Theory, University of California at Davis, California.
  8. Rice R. G., Do D. D., 1995. Applied Mathematics And Modeling For Chemical Engineers, John Wiley and Sons Inc., New York.

Details

Primary Language

English

Subjects

Software Engineering (Other)

Journal Section

Research Article

Publication Date

November 30, 2019

Submission Date

October 21, 2019

Acceptance Date

November 27, 2019

Published in Issue

Year 2019 Volume: 2 Number: 2

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
AMA
1.Keleş M, Pamuk S. Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis. KOJOSE. 2019;2(2):45-48. doi:10.34088/kojose.635255
Chicago
Keleş, Melike, and Serdal Pamuk. 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.
EndNote
Keleş M, Pamuk S (November 1, 2019) Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis. Kocaeli Journal of Science and Engineering 2 2 45–48.
IEEE
[1]M. Keleş and S. Pamuk, “Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis”, KOJOSE, vol. 2, no. 2, pp. 45–48, Nov. 2019, doi: 10.34088/kojose.635255.
ISNAD
Keleş, Melike - Pamuk, Serdal. “Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis”. Kocaeli Journal of Science and Engineering 2/2 (November 1, 2019): 45-48. https://doi.org/10.34088/kojose.635255.
JAMA
1.Keleş M, Pamuk S. Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis. KOJOSE. 2019;2:45–48.
MLA
Keleş, Melike, and Serdal Pamuk. “Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis”. Kocaeli Journal of Science and Engineering, vol. 2, no. 2, Nov. 2019, pp. 45-48, doi:10.34088/kojose.635255.
Vancouver
1.Melike Keleş, Serdal Pamuk. Perturbation Solutions of a Mathematical Model in Tumor Angiogenesis. KOJOSE. 2019 Nov. 1;2(2):45-8. doi:10.34088/kojose.635255