The first step of the Adams-Bashforth methods use this procedure.
n a Butcher tableau, this method is diagrammed with zeroes in the top row and a one in the bottom right. The first step of the Adams-Bashforth methods use this procedure. Huen's method is a variant on this procedure though his method's error scales with the interval cubed while this one scales with the interval squared. Implicit versions of this method and its variations are used for stiff equations. It is a first-order Runge-Kutta method. It corresponds to truncating the function's Taylor series to two terms, so the function evaluated at x plus delta x is equal to its value at x, plus delta x times the derivative at x. For 10 points, name this method of numerically approximating ODE solutions by approximating the function as linear over small intervals, that is named for a Swiss mathematician.
n a Butcher tableau, this method is diagrammed with zeroes in the top row and a one in the bottom right.
Euler's method [prompt on Runge-Kutta methods until it is read]