RKC21IvpOdeSolver.cpp

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*/


#include "RKC21IvpOdeSolver.hpp"

void RKC21IvpOdeSolver::CalculateNextYValue(AbstractOdeSystem* pAbstractOdeSystem,
                                                  double timeStep,
                                                  double time,
                                                  std::vector<double>& rCurrentYValues,
                                                  std::vector<double>& rNextYValues)
{
    /*
     * Apply Runge-Kutta-Chebyshev 1st order 2 stages method for each timestep in AbstractOneStepIvpSolver.
     * Calculates a vector containing the next Y value from the current one for each
     * equation in the system.
     */


     /*
     * The General RKC scheme:
     
    * w_{n0} = w_n;
    * w_{n1} = w_n + \tilde{\mu_1} * dt * F_{n0};
    * w_{nj} = (1 - mu_j - nu_j) w_n + mu_j*w_{n,j-1} + nu_j*w_{n,j-2} + \tilde{\mu_j}*dt*F_{n,j-1} + \tilde{\gamma_j}*dt*F_{n,0}, 
    * w_{n+1} = w_{ns}.
    * where:
    *       j = 2,...,s; 
    *       F_{nk} = F(t_n + c_k*dt, w_{nk});
    *       c_k = T_s(w_0)*Tp_k(w_0) / (Tp_s(w_0)*T_k(w_0)) with T_k/Tp_k are k-th Chebyshev polynomials/ derivatives of them
    *       w_0 is specific parameters
    * In RKC21, c_2 = \tilde{\mu_1}


     A decent reference on this method refer to Hundsdorfer, Willem, and Jan G. Verwer. Numerical solution of time-dependent advection-diffusion-reaction equations. Vol. 33. Springer Science & Business Media, 2013. P429
     */

     //RKC coefficients, hard-coded //TODO how to compute/where to store arbitrary RKC coefficients?

    const double mu1_tilde = 0.256134735558604;
    const double mu2 = 1.952097590002976;
    //const double nu2 = -b2/b0; canceled out in equation
    const double mu2_tilde =0.500000000000000;
    //const double gamma2_tilde = 0; never used in first order RKC

    const unsigned num_equations = pAbstractOdeSystem->GetNumberOfStateVariables();

    std::vector<double>& w0 = rCurrentYValues; // alias
    std::vector<double> w1(num_equations);
    std::vector<double>& w2 = rNextYValues; // alias
    std::vector<double> F0(num_equations);
    std::vector<double>& F1 = rNextYValues;

    // Work out w1
    pAbstractOdeSystem->EvaluateYDerivatives(time, w0, F0);

    for (unsigned i=0; i<num_equations; i++)
    {
        w1[i] = w0[i] + mu1_tilde * timeStep * F0[i];
    } 

    // Work next step
    pAbstractOdeSystem->EvaluateYDerivatives(time + mu1_tilde * timeStep, w1, F1);
    for (unsigned i=0; i<num_equations; i++)
    {
        w2[i] = (1-mu2) * w0[i] + mu2 * w1[i] + mu2_tilde * timeStep * F1[i];// + gamma2_tilde*timeStep*F0[i]; -> never used
    }
}


// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(RKC21IvpOdeSolver)