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Scaling of differential equations. (English) Zbl 1382.35001

Simula SpringerBriefs on Computing 2. Cham: Springer (ISBN 978-3-319-32725-9/pbk; 978-3-319-32726-6/ebook). xiii, 138 p. (2016).
The aim of the book is to scale differential equations in order to simplify the settings of parameters in numerical sumilations. The scaling method is presented in a large range of specific ODE and PDE models concerning epidemology, biochemistry, oscillations in classical mechanics and electric circuits, elasticity, viscous fluid flow, gas dynamics, water wave surfaces, thermal convection and porous media flow. Much of the mathematics is accomanied by computer codes (using the programming language Python and the Python package Parampool).

MSC:

35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
00A71 General theory of mathematical modeling
00A73 Dimensional analysis (MSC2010)
35A35 Theoretical approximation in context of PDEs
35Qxx Partial differential equations of mathematical physics and other areas of application
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Software:

Python; Parampool
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