Neural Computing and Applications

, Volume 31, Issue 7, pp 2233–2241 | Cite as

A reproducing kernel Hilbert space pseudospectral method for numerical investigation of a two-dimensional capillary formation model in tumor angiogenesis problem

  • M. EmamjomeEmail author
  • B. Azarnavid
  • H. Roohani Ghehsareh
Original Article


In the current work, an interesting and challenging mathematical model for a two-dimensional capillary formation model in tumor angiogenesis problem will be investigated numerically. The mathematical model describes progression of tumor angiogenic factor in a unit square space domain, namely the extracellular matrix. An efficient numerical technique is performed to approximate the numerical solution of the governing practical model. The method is based on reproducing kernel Hilbert spaces in the framework of the standard pseudospectral method. Using reproducing kernel Hilbert space operational matrices and elimination the treatment of complicated boundary conditions are the main advantages of the proposed method. Some illustrative examples are included to demonstrate the effectiveness and versatility of the technique to deal with the governing mathematical model in both linear and nonlinear models .


Reproducing kernel Hilbert space Pseudospectral method Capillary formation Tumor angiogenic factor 



The first author would like to thank “Golpayegan University of Technology” for supporting this work financially under the contract number 94500/3141. The authors would like to express their thankfulness to anonymous referees for their helpful constructive comments.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this manuscript.


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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • M. Emamjome
    • 1
    Email author
  • B. Azarnavid
    • 2
  • H. Roohani Ghehsareh
    • 3
  1. 1.Department of MathematicsGolpayegan University of TechnologyGolpayeganIran
  2. 2.Department of Computer SciencesShahid Beheshti University, G.C.TehranIran
  3. 3.Department of MathematicsMalek Ashtar University of TechnologyShahin ShahrIran

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