 Explicit Runge-Kutta method

An explicit Runge-Kutta method has $a_{ij}=0$ whenever $j\ge i$. Its stage matrix is strictly lower triangular: compute each Runge-Kutta stage using already known slopes, starting with $Y_1=y_n$. In contrast, an implicit Runge-Kutta method requires solving coupled stage equations, whose existence is addressed by stage solvability of an implicit Runge-Kutta method.