bvpSolve (version 1.1)

bvpSolve-package: Solvers for Boundary Value Problems (BVP) of Ordinary Differential Equations

Description

Functions that solve boundary value problems of a system of stiff ordinary differential equations (ODE) The functions provide (1) an interface to the FORTRAN code twpbvpC written by J.R. Cash, F. Mazzia and M.H. Wright, and (2) also implements a shooting method.

Details

ll{ Package: bvpSolve Type: Package Version: 1.1 License: GNU Public License 2 or above } The system of ODE's can be written as an Rfunction, or in compiled code (FORTRAN, C), similar as the initial value problems that are solved by integration routines from package deSolve. A large number of examples have been implemented to show the functionalities of the package.

• All test problems from the website of J.R. Cashhttp://www.ma.ic.ac.uk/~jcash/BVP_software/PROBLEMS.PDFare implemented in package vignette "bvpTests"
• Other test problems, inRcode are in the packagesdoc/examplesubdirectory.
• Test problems implemented in compiled code can be found in the packagesdoc/dynloadsubdirectory.
• Still more examples, both in R and compiled code are in the package vignetter "bvpSolve".

References

J.R. Cash and M.H. Wright, (1991) A deferred correction method for nonlinear two-point boundary value problems: implementation and numerical evaluation, SIAM J. Sci. Stat. Comput. 12, 971-989. Cash, J. R. and F. Mazzia, (2005) A new mesh selection algorithm, based on conditioning, for two-point boundary value codes. J. Comput. Appl. Math. 184 no. 2, 362--381. http://www.ma.ic.ac.uk/~jcash/BVP_software

See Also

bvptwp, a deferred correction method based on mono- implicit Runge-Kutta formulas and adaptive mesh refinement, based on conditioning to solve two-point boundary value problems (Cash and Mazzia, 2005). bvpshoot, a shooting method, using solvers from packages deSolve and rootSolve.

Examples

## show examples (see respective help pages for details)
example(bvptwp)
example(bvpshoot)

## open the directory with R- examples
browseURL(paste(system.file(package = "bvpSolve"), "doc/examples", sep = ""))

## open the directory with examples in compiled code
browseURL(paste(system.file(package = "bvpSolve"), "doc/dynload", sep = ""))

## show package vignette with how to use bvpSolve
## + source code of the vignette
vignette("bvpSolve")
edit(vignette("bvpSolve"))

## package vignette with the test problems from J.Cash
## + source code of the vignette
vignette("bvpTests")
edit(vignette("bvpTests"))


## show directory with source code of the vignettes
browseURL(paste(system.file(package = "bvpSolve"), "/doc", sep = ""))