Introduction

Both engineers and computational scientists alike will benefit greatly from having a standard test set for Initial Value Problems (IVPs) which includes documentation of the test problems, experimental results from a number of proven solvers, and Fortran subroutines providing a common interface to the defining problem functions. Engineers will be able to see at a glance which methods will be most effective for their class of problems. Researchers will be able to compare their new methods with the results of existing ones without incurring additional programming workload; they will have a reference with which their colleagues are familiar. This test set tries to fulfill these demands and tries to set a standard for IVP solver testing. We hope that the following features of this set will enable the achievement of this goal:

  • uniform presentation of the problems,
  • ample description of the origin of the problems,
  • robust interfaces between problem and drivers,
  • portability among different platforms,
  • contributions by people from several application fields,
  • presence of real-life problems,
  • being used, tested and debugged by a large, international group of researchers,
  • comparisons of the performance of well-known solvers,
  • interpretation of the numerical solution in terms of the application field,
  • ease of access and use.

There exist other test sets on the web, e.g., the Geneva test set by Ernst Hairer & Gerhard Wanner, the IVPtestset   by Jeff  Cash, the deTestSet by Karline Soetaert, Jeff Cash, Francesca Mazzia, an R-Cran package that include solvers and testset for stiff and nonstiff differential equations, and differential algebraic equations, the ODElab , a test frame for Ordinary Differential Equations by Nowak and Gebauer, the ODEpkg  Octave package by Thomas Treichl. Further collections of Test Problems can be found into the NSDTST and STDTST by Enright & Pryce, and PADETEST by Bellen.

 

Many of the test problems, the problem descriptions and the theory of solving differential equations are contained in the new book  Solving Differential Equations in R, Springer, 2012, by Karline Soetaert, Jeff Cash and Francesca Mazzia. The user is recommended to consult this reference which can be found at ' https://www.amazon.co.uk.  R is an open source programming language and software environment for statistical computing and graphics development. The R language is widely used and highly regarded by statisticians who use it to to develop statistical software. An aim of this book is to show that R also has some important advantages  as an environment when solving differential equations and this indicates that R is perhaps a more powerful language than was first appreciated.

 

 

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