Solvers for Boundary Value Problems (BVP) of Ordinary Differential Equations

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Description

Functions that solve boundary value problems of a system of ordinary differential equations (ODE)

The functions provide an interface to (1) the FORTRAN code twpbvpC written by J.R. Cash, F. Mazzia and M.H. Wright,

(2) to the FORTRAN codes colnew and colsys by respectively Bader and Ascher and Ascher, Christiansen and Russell,

and (3) also implement a shooting method.

Details

Package: bvpSolve
Type: Package
License: GNU Public License 2 or above

The system of ODE's can be written as an R function, 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. Cash (http://www.ma.ic.ac.uk/~jcash/BVP_software/PROBLEMS.PDF) are implemented in package vignette "bvpTests"

  • Other test problems, in R code are in the packages doc/example subdirectory.

  • Test problems implemented in compiled code can be found in the packages doc/dynload subdirectory.

  • Still more examples, both in R and compiled code are in the package vignette "bvpSolve".

Author(s)

Karline Soetaert (Maintainer)

Jeff Cash

Francesca Mazzia

References

Francesca Mazzia, Jeff R. Cash, Karline Soetaert (2014). Solving boundary value problems in the open source software R: Package bvpSolve. Opuscula mathematica, 34(2), 387–403. URL http://dx.doi.org/10.7494/OpMath.2014.34.2.387

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.

G. Bader and U. Ascher, (1987) a new basis implementation for a mixed order boundary value ode solver, siam j. scient. stat. comput. 8, 487-483.

U. Ascher, J. Christiansen and R. D. Russell, (1981) collocation software for boundary-value odes, acm trans. math software 7, 209-222.

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).

bvpcol, a collocation method to solve multi-point boundary value problems of ordinary differential equations. (Ascher et al., 1981).

bvpshoot, a shooting method, using solvers from packages deSolve and rootSolve.

diagnostics.bvpSolve, for a description of diagnostic messages.

plot.bvpSolve, for a description of plotting the output of the BVP solvers.

Examples

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## Not run: 
## show examples (see respective help pages for details)
example(bvptwp)
example(bvpshoot)
example(bvpcol)

## 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 = ""))

## End(Not run)