public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
Vector k1 = differentialEquasions(state, input, time);
Vector k2 = differentialEquasions(state + halfStep * k1, input, time + halfStep);
return(state + dt * k2);
}
public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
Vector diffs = differentialEquasions(state, input, time);
Vector prediction = state + dt * diffs;
return(state + halfStep * (diffs + differentialEquasions(prediction, input, time + dt))); // trapezoidal rule
}
public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
Vector k1 = differentialEquasions(state, input, time);
Vector k2 = differentialEquasions(state + oneThirdStep * k1, input, time + oneThirdStep);
Vector k3 = differentialEquasions(state + (-oneThirdStep * k1 + dt * k2), input, time + 2d * oneThirdStep);
Vector k4 = differentialEquasions(state + dt * (k1 - k2 + k3), input, time + dt);
return(state + oneEightStep * (k1 + 3f * k2 + 3f * k3 + k4));
}
public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
Vector k1 = differentialEquasions(state, input, time);
Vector k2 = differentialEquasions(state + halfStep * k1, input, time + halfStep);
Vector k3 = differentialEquasions(state + halfStep * k2, input, time + halfStep);
Vector k4 = differentialEquasions(state + dt * k3, input, time + dt);
Vector diff = oneSixStep * (k1 + 2d * k2 + 2d * k3 + k4);
return(state + diff);
}
public Launcher(DifferentialEquations differentialEquations, ExactSolution exactSolution, params ISolver[] solvers)
{
this.differentialEquations = differentialEquations;
this.exactSolution = exactSolution;
wrappers = new SolverWrapper[solvers.Length];
for (int i = 0; i < wrappers.Length; i++)
{
wrappers[i] = new SolverWrapper(solvers[i], differentialEquations);
}
}
public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
Vector k1 = dt * differentialEquasions(state, input, time);
Vector k2 = dt * differentialEquasions(state + a2[0] * k1, input, time + c[0] * dt);
Vector k3 = dt * differentialEquasions(state + a3[0] * k1 + a3[1] * k2, input, time + c[1] * dt);
Vector k4 = dt * differentialEquasions(state + a4[0] * k1 + a4[1] * k2 + a4[2] * k3, input, time + c[2] * dt);
Vector k5 = dt * differentialEquasions(state + a5[0] * k1 + a5[1] * k2 + a5[2] * k3 + a5[3] * k4, input, time + c[3] * dt);
Vector k6 = dt * differentialEquasions(state + a6[0] * k1 + a6[1] * k2 + a6[2] * k3 + a6[3] * k4 + a6[4] * k5, input, time + c[4] * dt);
Vector k7 = dt * differentialEquasions(state + a7[0] * k1 + a7[1] * k2 + a7[2] * k3 + a7[3] * k4 + a7[4] * k5 + a7[5] * k6, input, time + c[5] * dt);
//return state + b1[0] * k1 + b1[1] * k2 + b1[2] * k3 + b1[3] * k4 + b1[4] * k5 + b1[5] * k6 + b1[6] * k7;
return(state + b2[0] * k1 + b2[1] * k2 + b2[2] * k3 + b2[3] * k4 + b2[4] * k5 + b2[5] * k6 + b2[6] * k7);
}
public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
diffs.Push(differentialEquasions(state, input, time));
if (diffs.Count() < order)
{
return(starter.Solve(differentialEquasions, state, input, time, dt));
}
else
{
Vector sum = new Vector(state.Rows, 0d);
for (int i = 0; i < order; i++)
{
sum += coeffs[i] * diffs[i];
}
Vector ds = dt * sum;
return(state + ds);
}
}
static void Main(string[] args)
{
DifferentialEquations differentialEquation = (state, input, time) => (time * state); // y' = t * y
ExactSolution exactSolution = (time) => (Math.Exp(0.5 * time * time + 1));
Launcher launcher = new Launcher(differentialEquation, exactSolution,
new SolverEuler(),
new SolverEulerTrapezoidal(),
new SolverHeun(),
new SolverMidpoint(),
new SolverRK4(),
new SolverRK4Enhanced(),
new SolverDormandPrince(),
new SolverAdamsBashforth(5),
new SolverAdamsMoulton(5));
launcher.Test(2d, 0.001d);
Console.ReadKey();
}
public SolverWrapper(ISolver solver, DifferentialEquations differentialEquations)
{
this.Solver = solver;
this.differentialEquations = differentialEquations;
Data = new List <DataSample>();
}
public Vector Solve(DifferentialEquations differentialEquasions, Vector state, double input, double time, double dt)
{
Vector differentials = differentialEquasions(state, input, time);
return(state + dt * differentials);
}
