# R/SoilR.euler.R In SoilR: Models of Soil Organic Matter Decomposition

#### Defines functions SoilR.euler

```#
# vim:set ff=unix expandtab ts=2 sw=2:
SoilR.euler=function
### This function can solve arbitrary first order ode systems with the euler forward
### method and an
### adaptive time-step size control given a tolerance for the deviation of a coarse and fine
### estimate of the change in y for the next time step.
### It is an alternative to \code{\link{ode}} and has the same interface.
### It is much slower than ode and should probably be considered less capable in solving stiff ode systems.
### However it has one main advantage, which consists in its simplicity.
### It is quite easy to see what is going on inside it.
### Whenever you don't trust your implementation of another (more efficient but probably also more complex)
### ode solver, just compare the result to what this method computes.
(times,		##<< A row vector containing the points in time where the solution is sought.
ydot,		##<< The function of y and t that computes the derivative for a given point in time and a column vector y.
startValues		##<< A column vector with the initial values.
){
inc=1.5
tol=10**(-10) # this is the tolerance that is allowed for the difference of estimation and solution for the
#next step
ttol=10**(-10) #this is only a technical value that avoids an infinite loop caused by roundoferrors for time
minstep=10**(-5) #the smalles timestep allowed to avoid locking

#determine the number of unknowns
n=nrow(startValues)
#determine the number of time values for which the solution is sought
tn=length(times)
#we give a startvalue for the timestepsize
Y=matrix(nrow=n,ncol=tn)
y=startValues
Y[,1]=y
#now devide the time in to steps
for (j in 2:tn){
targettime=times[j]
t=times[j-1]
stepsize=(targettime-t)/10
y=Y[,j-1] #we always start at the boundaries of timesteps
while (t< targettime-ttol){
#store in case we have to revert the next step
y0=y
dy=stepsize*ydot(y,t)
#make a prediction yp=y(t+stepsize)
yp=y+dy
#now devide the stepsize in k subintervals and compute the value
# fpr y(t+stepsize) in k steps
k=4
smallstep=stepsize/k
for (i in 1:k){
t=t+smallstep
dy=smallstep*ydot(y,t)
y=y+dy
}
#compare the results
ydiff=sum((yp-y)*(yp-y))
if (ydiff>tol){
# do it again
t=t-stepsize
y=y0
#in smaller steps
stepsize=stepsize/2
}
else{
# become bolder but look ahead a bit
rest=targettime-t
planedstep=inc*stepsize
# if the target time is far enough ahead for the planed timestep
if (rest>planedstep)
#increase timestep but with a look at the target
#because we want to avoid a very small last timestep
if (rest-planedstep<minstep)
#since the planed step would bring us too near the target but not
#quite there we decide to suggest two steps instead with the
{stepsize=rest/2}
else
# or prooced as normal
{stepsize=stepsize*inc}
#otherwise make a direct leap to the next targettime
else{stepsize=rest}
}
}
Y[,j]=y
}
Yt=t(Y)
return(Yt)
}
```

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SoilR documentation built on May 29, 2017, 10:57 a.m.