mcODE-package {mcODE}

Monte Carlo Integration of First Order ODEs

Description

Monte Carlo solution of first order differential equations and confidence intervals for the solutions.

Details

ODE.MVT can solve any first order differential equation of the form g' = F(x, g) with initial condition g(x0) = g0, provided conditions are satisfied for existence and uniqueness of the solution. Confidence intervals for the solution can be obtained through use of ODE.MVT.agg. An alternate method due to Akhtar et al is implemented in ODE.ADA.

Author(s)

Author: W.J. Braun

Maintainer: W.J. Braun

References

Akhtar, M. N., Durad, M. H., and Ahmed, A. (2015). Solving initial value ordinary differential equations by Monte Carlo method. Proc. IAM, 4:149-174.

Braun, W. J. (2024) Monte Carlo integration of first order ordinary differential equations. Preprint.

See Also

deSolve

Examples

# Solve g' = F(x, g) on (0, 1] with g(0) = -1/1000001
G <- function(x, g) {
    -1000*g + 3000 - 2000*exp(-x)
}
T <- 1
x0 <- 0
g0 <- -1/1000001
nMVT <- 5000
ghat <- ODE.MVT(G, initvalue = g0, endpoint = T, initpoint = x0, Niter = 2, npoints = nMVT)
plot(ghat, type = "l")