public double LOperator(MathFunction yx, double x)
{
MathFunction der2 = yx.Derivative(2),
der1 = yx.Derivative(1);
return(der2.Calculate(x) + PX.Calculate(x) * der1.Calculate(x) +
QX.Calculate(x) * yx.Calculate(x));
}
public double Solve(Equasion eq, double a, double b)
{
MathFunction func = eq.Left - eq.Right;
MathFunction der1 = func.Derivative(1),
der2 = func.Derivative(2);
if (!IsSuitable(der1, a, b) ||
!IsSuitable(der2, a, b))
throw new Exception("Method can not be applied!");
MathFunction ksi = IterationFunc(der1, a, b);
double x0 = InitialX(func, a, b);
return GenericIterationMethod(func, ksi, a, b, x0);
}
public double Solve(Equasion eq, double a, double b)
{
MathFunction func = eq.Left - eq.Right;
MathFunction der1 = func.Derivative(1),
der2 = func.Derivative(2);
if (!IsSuitable(der1, a, b) ||
!IsSuitable(der2, a, b))
{
throw new Exception("Method can not be applied!");
}
double c = SuitableRandomArgumnent((double x) => { return(func.Calculate(x) * der2.Calculate(x) > 0); }, a, b);
MathFunction ksi = IterationFunc(func, a, b, c);
double x0 = InitialX(func, a, b, c);
return(GenericIterationMethod(func, ksi, a, b, x0));
}
protected virtual double GenericIterationMethod(MathFunction func, MathFunction ksi, double a, double b, double x0)
{
double xn = x0, counter = 0;
double fDerivativeMin = func.Derivative(1).MinValue(a, b);
MathFunction iterFunc = new XFunction(1.0d) + ksi * func;
do
{
xn = iterFunc.Calculate(xn);
counter++;
} while (counter < maxIterationCount && !(Math.Abs(func.Calculate(xn)) / fDerivativeMin <= epsilanIter));
if (counter == maxIterationCount)
{
return(xn); // double.PositiveInfinity;
}
return(xn);
}
private static MathFunction <BigFloat> CalculateFunction(int power, BigFloat point, ref MathFunction <BigFloat> function, ref int curPower)
{
function = function.Derivative(power - curPower);
curPower = power;
BigFloat value = function.Calculate(point);
BigInteger fact = Factorial.Calculate(power);
value /= fact;
if (power == 0)
{
return(value);
}
else if (power == 1)
{
return(value * (new XFunction <BigFloat>(1.0) - point));
}
else
{
return(new PowerFunction <BigFloat>(value, new XFunction <BigFloat>(1.0) - point, (BigFloat)power));
}
}
protected double InitialX(MathFunction func, double a, double b)
{
return SuitableRandomArgumnent((double arg) => { return func.Calculate(arg) * func.Derivative(2).Calculate(arg) < 0; }, a, b);
}