Scaling of Differential Equations Hans Petter Langtangen, Geir K. Pedersen
Share this page:-
We need Your Support, Kindly Share this Web Page with Other Friends
Congratulations, the link is avaliable for free download.
About this book :-
Scaling of differential equations is basically a simple mathematical process,consisting of the chain rule for differentiation and some algebra. The choice of scales, however, is a non-trivial topic, which may cause confusion among practitioners without extensive experience with scaling.
How to choose scales is unfortunately not well treated in the literature. Most of the times, authors just state scales without proper motivation. The choice of scales is highly problem-dependent and requires knowledge of the characteristic features of the solution or the physics of the problem. The present notes aim at explaining“all nuts and bolts” of the scaling technique, including choice of scales, the algebra, the interpretation of dimensionless parameters in scaled models, and how scaling impacts software for solving differential equations. Traditionally, scaling was mainly used to identify small parameters in mathematical models, such that perturbation methods based on series expansions in terms of the small parameters could be used as an approximate solution method for differential equations.
Nowadays, the greatest practical benefit of scaling is related to running numerical simulations, since scaling greatly simplifies the choice of values for the input data and makes the simulations results more widely applicable. The number of parameters in scaled models may be much less than the number of physical parameters in the original model. The parameters in scaled models are also dimensionless and expressions of physical effects rather than levels of individual effects. Set-ting meaningful values of a few dimensionless numbers is much easier than determining physically relevant values for the original physical parameters.
Book Detail :-
This book has following details information.
Title:
Scaling of Differential Equations Hans Petter Langtangen, Geir K. Pedersen by NA
Publisher:
Springer
Series:
FreeCompBooks
Year:
2016
Pages:
151
Type:
PDF
Language:
English
ISBN-10 #:
3319327259
ISBN-13 #:
978-3319327259
Country:
Pakistan
License:
CC BY-NC 4.0
Get this book from Amazon
About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
Dimensions and units - Ordinary differential equation models - Basic partial differential equation models - Advanced partial differential equation models
Note :-
We are not the owner of this book/notes. We provide it which is already avialable on the internet. For any further querries please contact us. We never SUPPORT PIRACY. This copy was provided for students who are financially troubled but want studeing to learn.
If You Think This Materials Is Useful, Please get it legally from the PUBLISHERS.
Thank you.
Now please OPEN for DOWNLOAD the BOOK.
'
Similar
Differential Equations
Books