Introduction

Numerical methods to solve ordinary differential equations.

Methods comes with Butcher tableaus. Note that (embedded) tableaus come with a non-standard notation in lower left quadrant (p), showing the order of the weights ($b$).

Butcher tableau:

$c^T$	$A$
p	$b$

Usage

Solve $y\rq=y$, for $t=[0;4]$, with initial value $y(0)=1$

auto function = [](
	Real const& y,
	[[maybe_unused]] Real const& t
	) -> Real
{
	return y;
};

Real y{ 1.q };

// h, fixed step size
Real const h{ 0.02q };

Real const t_max{ 4.q };
std::uint64_t i{ 0 };
do {
	y = ODE::Euler::Forward<Real>( function, h, y );
} while ( ++i * h < t_max );
std::cout << "Euler: y(" << i * h << " ) =" << y << '\n';

Output:

Steps take: 200
Euler: y( 4 ) = 52.4849

More examples are included in the $main.cpp$ file.

Requirement

C++23 (for 128bit decimal numbers)

Additional

Output of the Fitzhugh oscillator example in $main.cpp$.