forward_euler Function

public function forward_euler(F, t, U0) result(U)

function for integrating vector first order ODEs of the form: $$\frac{d\mathbf{U}}{dt}=\mathbf{F}\left(\mathbf{U},t\right)$$ using the forward (explicit) euler method.

Arguments

Type	Intent	Optional	Attributes		Name
public function F(U, t) result(dU) function $\mathbf{F}$ of the system Arguments Type Intent Optional Attributes Name real, intent(in) :: U(:) value of the unknown function $\mathbf{U}(t)$ real, intent(in) :: t independent variable $t$ Return Value real, (size(U)) derivative of $\mathbf{y}$
real,	intent(in)			::	t(0:)	array of times $t_0,t_1,\dots,t_N$where the numerical solution will be evaluated.
real,	intent(in)			::	U0(:)	initial conditions $\mathbf{U}(t_0)$

Return Value real, (0:ubound(t,1),size(U0))

solution array $U_j(t_i)$ such that the the row $i$ and column $j$ stands for the $j$th component of the vector solution $\mathbf{U}$ at time $t_i$.