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Solving differential equations in R. (English) Zbl 1252.65138
Use R!. Berlin: Springer (ISBN 978-3-642-28069-6/pbk; 978-3-642-28070-2/ebook). xvi, 248 p. (2012).
The book in general deals with the numerical methods implemented to different differential problems. One can find here a descriptions of differential equations of different types (ordinary and partial differential equations, differential algebraic equations, delay differential equations), as well as the descriptions of fairly well-known and widely used numerical methods for their solution. The main thing that differentiates this book from others is the fact that the authors propose to use for this purpose some non-specific programming environment such as $$R$$.
As it is known $$R$$ is an open source programming language and software environment for statistical computing and graphics. The $$R$$ language is widely used among statisticians for developing statistical software and data analysis. From the other side, $$R$$ is highly extensible through the use of user-submitted packages for specific functions or specific areas of study. $$R$$ has stronger object-oriented programming facilities than most statistical computing languages. So many users think of $$R$$ as a statistics system. However, the authors manage to convince the reader about the ability to use this software to solve differential problems. Moreover, to some extent, they show its potential benefits.

##### MSC:
 65L99 Numerical methods for ordinary differential equations 35-04 Software, source code, etc. for problems pertaining to partial differential equations 65Y15 Packaged methods for numerical algorithms 68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65N99 Numerical methods for partial differential equations, boundary value problems 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
##### Software:
BvpSolve; COLSYS; deSolve; deTestSet; diffEq; LSODE; MEBDF; R; RootSolve; SPARSKIT; VODE
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