The method of lines for the numerical solution of a mathematical model for capillary formation: The role of endothelial cells in the capillary

DOI10.1016/j.amc.2006.08.024zbMath1114.65111OpenAlexW2136398575MaRDI QIDQ876669

Arzu Erdem, Serdal Pamuk

Publication date: 26 April 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.024

zbMATH Keywords

numerical examplesmethod of linestumor angiogenesiscapillary formation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Cell biology (92C37) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Iterative operator splitting method for capillary formation model in tumor angiogenesis problem: Analysis and application ⋮ Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method ⋮ Finite difference method for capillary formation model in tumor angiogenesis ⋮ The method of lines for solution of the one-dimensional wave equation subject to an integral conservation condition ⋮ The method of lines for the numerical solution of a mathematical model for capillary formation: The role of tumor angiogenic factor in the extra-cellular matrix ⋮ A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams ⋮ روشی بدون شبکه برای حل عددی مدل ریاضی از مرتبه مشتق کسری تشکیل مویرگ در تومور رگزایی ⋮ Numerical analysis of a mathematical model for capillary formation in tumor angiogenesis using a meshfree method based on the radial basis function ⋮ Method of lines solutions of the parabolic inverse problem with an overspecification at a point

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma
• Solution of the porous media equation by Adomian's decomposition method
• On the validity and stability of the method of lines for the solution of partial differential equations
• An application for a generalized KdV equation by the decomposition method
• The decomposition method for continuous population models for single and interacting species
• An application for linear and nonlinear heat equations by Adomian's decomposition method
• A good spatial discretisation in the method of lines
• QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS
• Antireduction and exact solutions of nonlinear heat equations
• MOL solvers for hyperbolic PDEs with source terms