Efficient resolution of metastatic tumor growth models by reformulation into integral equations

DOI10.3934/dcdsb.2015.20.445zbMath1310.35230OpenAlexW2313930895MaRDI QIDQ489258

Niklas Hartung

Publication date: 20 January 2015

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2015.20.445

zbMATH Keywords

Volterra integral equationnumerical approximationstructured population modelsMcKendrick/Von Foerster equationmetastatic growth

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Population dynamics (general) (92D25) Volterra integral equations (45D05)

Related Items (5)

Stability and boundedness of numerical approximations to Volterra integral equations ⋮ A sufficient condition for the stability of direct quadrature methods for Volterra integral equations ⋮ A numerical method for linear Volterra integral equations on infinite intervals and its application to the resolution of metastatic tumor growth models ⋮ Modeling metastatic tumor evolution, numerical resolution and growth prediction ⋮ Numerical optimal control of a size-structured PDE model for metastatic cancer treatment

Cites Work

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• Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis
• Mathematical and numerical analysis for a model of growing metastatic tumors
• A model describing the growth and the size distribution of multiple metastatic tumors
• A perspective on the numerical treatment of Volterra equations
• Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers
• Fast Numerical Solution of Nonlinear Volterra Convolution Equations
• Runge-Kutta Theory for Volterra Integral Equations of the Second Kind

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