public Vector computeSolutionVectorWithMultipleSteps(Vector initial, OrdinaryDifferentialEquation ode, double startTime, double endTime, double step)
{
double tempTime = startTime;
int N = Convert.ToInt32((endTime - startTime) / step) + 1;
Vector tempSolution = initial;
Vector solution = new Vector(N);
solution[0] = initial[0];
Vector temp = new Vector(1);
for (int i = 1; i < N; i++)
{
temp[0] = solution[i - 1];
solution[i] = computeSolutionForNextStep(temp, ode, tempTime, tempTime + step)[0];
tempTime += step;
}
if (!GeneralHelper.isXAlmostEqualToY(startTime + (N-1) * step, endTime))
{
tempTime = startTime + N * step;
tempSolution = computeSolutionForNextStep(tempSolution, ode, tempTime, endTime);
}
return solution;
}
public Vector computeSolutionForNextStep(Vector initial,OrdinaryDifferentialEquation ode, double startTime, double endTime)
{
Vector tempSolution = initial;
Vector evaluatedODE = ode.evaluateOrdinaryDifferentialEquation(tempSolution, startTime);
double deltaTime = endTime - startTime;
for(int i = 0; i < 5; i++)
{
double nextTimeStep = startTime + B[i] * deltaTime;
evaluatedODE = (Vector) (A[i] * evaluatedODE) + ode.evaluateOrdinaryDifferentialEquation(tempSolution, nextTimeStep);
tempSolution = tempSolution + (Vector)(C[i] * deltaTime * evaluatedODE);
}
return tempSolution;
}
public Vector computeSolutionWithMultipleSteps(Vector initial, OrdinaryDifferentialEquation ode, double startTime, double endTime, double step)
{
double tempTime = startTime;
int N = Convert.ToInt32((endTime - startTime)/ step);
Vector tempSolution = initial;
for(int i = 1; i <= N; i++)
{
tempSolution = computeSolutionForNextStep(tempSolution, ode, tempTime, tempTime + step);
tempTime += step;
}
if (!GeneralHelper.isXAlmostEqualToY(startTime + N * step, endTime))
{
tempTime = startTime + N * step;
tempSolution = computeSolutionForNextStep(tempSolution, ode, tempTime, endTime);
}
return tempSolution;
}
public void evaluate()
{
//Anfangsbedingung
Vector initial = new Vector(1);
initial[0] = -1.0;
List<Func<double, double, double>> mySystem = new List<Func<double, double, double>>();
mySystem.Add(derivativeFunction);
OrdinaryDifferentialEquation testEquation = new OrdinaryDifferentialEquation(mySystem);
IODESolver odeSolver = new RungeKuttaSolver();
double[] errorList = new double[10];
for (int i = 1; i <= 10; i++)
{
double timeStep = Math.Pow(2.0, -i);
Vector res = odeSolver.computeSolutionVectorWithMultipleSteps(initial, testEquation, 1.0, 2.0, timeStep);
//Vector exact = null; //hier die exacte auswertung
//double error = (res - exact) * (res - exact);
}
}
