GRL2IvpOdeSolver.cpp

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/*
Megan E. Marsh, Raymond J. Spiteri
Numerical Simulation Laboratory
University of Saskatchewan
December 2011
Partial support provided by research grants from the National
Science and Engineering Research Council (NSERC) of Canada
and the MITACS/Mprime Canadian Network of Centres of Excellence.
*/
 
#include <cstdio>
#include <cmath>
 
#include "GRL2IvpOdeSolver.hpp"
void GRL2IvpOdeSolver::CalculateNextYValue(AbstractOdeSystem* pAbstractOdeSystem,
                                                  double timeStep,
                                                  double time,
                                                  std::vector<double>& rCurrentYValues,
                                                  std::vector<double>& rNextYValues)
{
    /*
     * Apply GRL2 second-order method for each time step in AbstractOneStepIvpSolver.
     * Calculates a vector containing the next Y value from the current one for each
     * equation in the system.
     */
    const double delta = 1.0e-8; // The step for numerical jacobian calculation
 
    const unsigned num_equations = pAbstractOdeSystem->GetNumberOfStateVariables();
 
    if (mEvalF.size() != num_equations)
    {
        mEvalF.resize(num_equations);
        mPartialF.resize(num_equations);
        mTemp.resize(num_equations);
        mYinit.resize(num_equations);
    }
 
    rNextYValues = rCurrentYValues;
    double ysave;
 
    mYinit = rNextYValues;
    pAbstractOdeSystem->EvaluateYDerivatives(time, rNextYValues, mEvalF);
 
    for (unsigned i=0; i<num_equations; i++)
    {
        rNextYValues[i]=rNextYValues[i]+delta;
        pAbstractOdeSystem->EvaluateYDerivatives(time, rNextYValues, mTemp);
        mPartialF[i]=(mTemp[i]-mEvalF[i])/delta;
        rNextYValues[i]=rNextYValues[i]-delta;
    }
    // Midpoint
    for (unsigned i=0; i<num_equations; i++)
    {
        if (fabs(mPartialF[i])<delta)
        {
            rNextYValues[i]=rNextYValues[i]+0.5*mEvalF[i]*timeStep;
        }
        else
        {
            rNextYValues[i]=rNextYValues[i]+(mEvalF[i]/mPartialF[i])*(exp(mPartialF[i]*0.5*timeStep)-1);
        }
    }
    //Second half of the method
    for (unsigned i=0; i<num_equations; i++)
    {
        ysave = rNextYValues[i];
        rNextYValues[i]=mYinit[i];
        pAbstractOdeSystem->EvaluateYDerivatives(time, rNextYValues, mTemp);
        mEvalF[i]=mTemp[i];
 
        rNextYValues[i]=rNextYValues[i]+delta;
        pAbstractOdeSystem->EvaluateYDerivatives(time, rNextYValues, mTemp);
        mPartialF[i]=(mTemp[i]-mEvalF[i])/delta;
        rNextYValues[i]=ysave;
    }
 
    //Final step update
    for (unsigned i=0; i<num_equations; i++)
    {
        if (fabs(mPartialF[i])<delta)
        {
            rNextYValues[i]=mYinit[i]+mEvalF[i]*timeStep;
        }
        else
        {
            rNextYValues[i]=mYinit[i]+(mEvalF[i]/mPartialF[i])*(exp(mPartialF[i]*timeStep)-1);
        }
    }
}
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(GRL2IvpOdeSolver)