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 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);
}
