Van der Houwen, S.B, (1980) On the Internal Stage Runge-Kutta Methods for Large m-Values. Zeitschrift für Angewandte Mathematik und Mechanik, 60, 479-485.

has been cited by the following article:

• TITLE: Analysis on a Mathematical Model for Tumor Induced Angiogenesis

  AUTHORS: Richard C. Ewool, Zachariah Sinkala

  KEYWORDS: Explicit Stabilized Runge-Kutta Methods, Angiogenesis, Inhibitors, Rat Cornea, Source Term

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.7, June 25, 2014

  ABSTRACT: Tumor-induced angiogenesis is the process by which unmetastasized tumors recruit red blood vessels by way of chemical stimuli to grow towards the tumor for vascularization and metastasis. We model the process of tumor-induced angiogenesis at the tissue level using ordinary and partial differential equations (ODEs and PDEs) that have a source term. The source term is associated with a signal for growth factors from the tumor. We assume that the source term depends on time, and a parameter (time parameter). We use an explicit stabilized Runge-Kutta method to solve the partial differential equation. By introducing a source term into the PDE model, we extend the PDE model used by H. A. Harrington et al. Our results suggest that the time parameter could play some role in understanding angiogenesis.