double Integration::stepRectangle(double eps) const
{
Derivator* derivator = new Derivator(f);
Func g = derivator->derive();
double max = g.maxModulo(ab);
delete derivator;
return (2*eps / (max*(ab.end() - ab.begin())));
}
double Integration::stepSimpson(double eps) const
{
Derivator* derivator = new Derivator(f);
Func g = derivator->derive(4);
double max = g.maxModulo(ab);
delete derivator;
return pow(180*eps / (max*(ab.end() - ab.begin())), 0.25);
}
double Integration::stepTrapezoid(double eps) const
{
Derivator* derivator = new Derivator(f);
Func g = derivator->derive(2);
double max = g.maxModulo(ab);
delete derivator;
return sqrt(12*eps / (max*(ab.end() - ab.begin())));
}
double Integration::errorSimpson() const
{
Derivator* derivator = new Derivator(f);
Func g = derivator->derive(4);
double max = g.maxModulo(ab);
double h = (ab.end() - ab.begin()) / 4;
delete derivator;
return (max * pow(h, 4) * (ab.end() - ab.begin())) / 180;
}
double Integration::errorRectangle() const
{
Derivator* derivator = new Derivator(f);
Func g = derivator->derive();
double max = g.maxModulo(ab);
double h = (ab.end() - ab.begin()) / 4;
delete derivator;
return (max * h * (ab.end() - ab.begin())) / 2;
}
