Abstract
R has three packages that are useful for solving partial differential equations. The R package ReacTran offers grid generation routines and the discretization of the advective-diffusive transport terms on these grids. In this way, the PDEs are either rewritten as a set of ODEs or as a set of algebraic equations. When solving the PDEs with the method of lines (MOL), the time integration can be performed using specially-designed initial value problem solvers from the R package deSolve. When all derivatives have been approximated, functions from the R package rootSolve can efficiently solve the algebraic equations. We show how to solve in R the well-known heat equation (parabolic), the wave equation (hyperbolic), Laplace’s equation (elliptic), and the advection equation. We then give some more complex examples. Most partial differential equations are defined in cartesian coordinates, but some problems are much better represented in other coordinate systems. These problems can be solved efficiently in R as well.
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Notes
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The latter requirement is unfortunate and it may require some trial and error to find a good value; however, if too little memory is allocated, the solver may stop with a message telling the size this vector should minimally have.
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From http://en.wikipedia.org/wiki/Laplace’s_equation.
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Soetaert, K., Cash, J., Mazzia, F. (2012). Solving Partial Differential Equations in R. In: Solving Differential Equations in R. Use R!. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28070-2_9
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