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100 4 SolvingOrdinaryDifferentialEquations
Fig.4.1 Mesh in timewithcorrespondingdiscretevalues (unknowns)
Fig.4.2 Illustrationof a forwarddifferenceapproximation to thederivative
Third, derivatives are to be replaced byfinite differences. To this end,weneed
to know specific formulas for howderivatives can be approximated by finite dif-
ferences. One simple possibility is to use the definition of the derivative fromany
calculusbook,
u0.t/D lim
t!0 u.tC t/ u.t/
t :
Atanarbitrarymeshpoint tn thisdefinitioncanbewrittenas
u0.tn/D lim
t!0 unC1 un
t :
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book Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python"
Programming for Computations – Python
A Gentle Introduction to Numerical Simulations with Python
- Title
- Programming for Computations – Python
- Subtitle
- A Gentle Introduction to Numerical Simulations with Python
- Authors
- Svein Linge
- Hans Petter Langtangen
- Publisher
- Springer Open
- Date
- 2016
- Language
- English
- License
- CC BY-NC 4.0
- ISBN
- 978-3-319-32428-9
- Size
- 17.8 x 25.4 cm
- Pages
- 248
- Keywords
- Programmiersprache, Informatik, programming language, functional, imperative, object-oriented, reflective
- Category
- Informatik