I have to solve the Black-Scholes equation,
$\textrm{d}X\left(t\right)=\lambda X\left(t\right)\textrm{d}t+\mu X\left(t\right)\textrm{d}W\left(t\right),$
by making use of a RK method (in Python). Since this equation is analytically solvable, I could compare both solutions eventually.
Nonetheless, I would like to encounter a 4th order RK method that could solve this equation rightly (i.e., in comparison to the analytical solution). This is because I will have to use this method to solve deterministic equations as well.
Incidentally, I've already tried to code several RK methods such as this one: 4th order Runge-Kutta Scheme for Stochastic Differential Equations (the classic one) or the 3/8 method. Both however give solutions that don't agree with the analytical one whatsoever.