public void ExponentSolveToGearTest()
{
foreach (var sp in Ode.GearBDF(0,
1,
(t, x) => - x,
new Options {
RelativeTolerance = 1e-4
}).SolveTo(10))
{
Assert.IsTrue(Math.Abs(sp.X[0] - Math.Exp(-sp.T)) < 1e-3);
}
}
public void ExponentSolveToRKTest()
{
foreach (var sp in Ode.RK547M(0,
1,
(t, x) => - x,
new Options {
RelativeTolerance = 1e-3
}).SolveTo(1000))
{
Assert.IsTrue(Math.Abs(sp.X[0] - Math.Exp(-sp.T)) < 1e-2);
}
}
public void ExponentSolveToArrayTest()
{
var arr = Ode.RK547M(0,
1,
(t, x) => - x,
new Options {
RelativeTolerance = 1e-3
}).SolveTo(1000).ToArray();
foreach (var sp in arr)
{
Assert.IsTrue(Math.Abs(sp.X[0] - Math.Exp(-sp.T)) < 1e-2); // AbsTol instead of 1e-4
}
}
/// <summary>Implementation of Runge-Kutta algoritm with per-point accurancy control from
/// Dormand and Prince article.
/// (J.R.Dormand, P.J.Prince, A family of embedded Runge-Kuttae formulae)</summary>
/// <param name="tstart">Left end of current time span</param>
/// <param name="tfinal">Final time</param>
/// <param name="x0">Initial phase vector value</param>
/// <param name="f">System right parts vector function</param>
/// <example>Let our problem will be:
/// dx/dt=y+1,
/// dy/dt=-x+2.
/// x(0)=0, y(0)=1.
/// To solve it, we just have to write
/// <code>
/// var sol=Ode.RK547M(0,new Vector(0,1),(t,x)=>new Vector(y+1,-x+2));
/// </code>
/// and then enumerate solution point from <see cref="IEnumerable{SolutionPoint}"/>.
/// </example>
/// <returns>Endless sequence of solution points</returns>
public static IEnumerable <SolutionPoint> RK547M(double tstart, double tfinal, Vector x0, Func <double, Vector, Vector> f, Options opts)
{
if (opts == null)
{
throw new ArgumentException("opts");
}
if (opts.MaxStep == double.MaxValue)
{
opts.MaxStep = (tfinal - tstart) * 1e-2;
}
return(Ode.RK547M(tstart, x0, f, opts).SolveFromTo(tstart, tfinal));
}