public static CauchyProblemResult AdamsBashforthMethodsSolve(Func<double, Vector, Vector> f, Vector initValue, double maxTime, int intervals)
{
double deltaTime = maxTime / intervals;
CauchyProblemResult result = new CauchyProblemResult(deltaTime);
CauchyProblemResult firstResult = CauchyProblemSolver.HeunMethodSolve(f, initValue, deltaTime * 2, 2);
foreach (Vector res in firstResult.Results)
{
result.AddResult(res);
}
for (int t = 3; t <= intervals; t++)
{
int lastIndex = result.Results.Count - 1;
Vector u_n_2 = result.Results[lastIndex - 2];
Vector u_n_1 = result.Results[lastIndex - 1];
Vector u_n = result.Results[lastIndex];
Vector u = u_n + (deltaTime / 12) * (23 * f(deltaTime * lastIndex, u_n) - 16 * f(deltaTime * (lastIndex - 1), u_n_1) + 5 * f(deltaTime * (lastIndex - 2), u_n_2));
result.AddResult(u);
}
return result;
}
public static CauchyProblemResult HeunMethodSolve(Func<double, Vector, Vector> f, Vector initValue, double maxTime, int intervals)
{
double deltaTime = maxTime / intervals;
CauchyProblemResult result = new CauchyProblemResult(deltaTime);
Vector v = initValue;
result.AddResult(v);
for (double t = deltaTime; t <= maxTime; t += deltaTime)
{
Vector prevV = result.Results.Last();
Vector prevF = f(t, prevV);
v = prevV + (deltaTime / 2) * (f(t, prevV + deltaTime * prevF) + prevF);
result.AddResult(v);
}
return result;
}
private CauchyProblemResult NewmarkSolver(Matrix massMatrix, Matrix stiffnessMatrix, Vector initValue, double gamma, double alfa, double maxTime, int intervals)
{
double deltaTime = maxTime / intervals;
CauchyProblemResult result = new CauchyProblemResult(deltaTime);
double a1 = (2 / (deltaTime * deltaTime * gamma));
double a2 = (2 / (deltaTime * gamma));
double a3 = ((1 / gamma) - 1);
double a4 = deltaTime * (1-alfa);
double a5 = deltaTime * alfa;
Vector u = initValue;
Vector du = new Vector(initValue.Length);
Vector ddu = massMatrix.LUalgorithm((-1) * stiffnessMatrix * initValue);
result.AddResult(u);
Matrix K = massMatrix * a1 + stiffnessMatrix;
for (double t = deltaTime; t <= maxTime; t += deltaTime)
{
Vector uprev = u;
Vector duprev = du;
Vector dduprev = ddu;
Vector F = massMatrix * (a1 * uprev + a2 * duprev + a3 * dduprev);
u = K.LUalgorithm(F);
ddu = a1 * (u - uprev) - a2 * duprev - a3 * dduprev;
du = duprev + a4 * dduprev + a5 * ddu;
ApplyNonlinearity(massMatrix, stiffnessMatrix, ref u, ref du, ref ddu, a1, a2, a3, a4, a5);
result.AddResult(u);
}
return result;
}
public static CauchyProblemResult GirMethodsSolve(Func<double, Vector, Vector> f, Vector initValue, double maxTime, int intervals)
{
double eps = 0.001;
double deltaTime = maxTime / intervals;
CauchyProblemResult result = new CauchyProblemResult(deltaTime);
CauchyProblemResult firstResult = CauchyProblemSolver.HeunMethodSolve(f, initValue, deltaTime * 2, 2);
foreach (Vector res in firstResult.Results)
{
result.AddResult(res);
}
for (int t = 3; t <= intervals; t++)
{
int lastIndex = result.Results.Count - 1;
Vector u_n_2 = result.Results[lastIndex - 2];
Vector u_n_1 = result.Results[lastIndex - 1];
Vector u_n = result.Results[lastIndex];
Vector u = u_n + (deltaTime / 12) * (23 * f(deltaTime * lastIndex, u_n) - 16 * f(deltaTime * (lastIndex - 1), u_n_1) + 5 * f(deltaTime * (lastIndex - 2), u_n_2));
Vector prevU = new Vector(u.Length);
Vector constU = (18 * u_n - 9 * u_n_1 + 2 * u_n_2) / 11;
while (Vector.Norm(u - prevU) > eps)
{
prevU = u;
u = ((6 * deltaTime) / 11) * f(deltaTime * lastIndex, prevU) + constU;
}
result.AddResult(u);
}
return result;
}
