The explicit methods are those where the matrix is lower triangular. The Euler method is first order. The lack of stability and accuracy limits its popularity mainly to use as a simple introductory example of a numeric solution method. The (explicit) midpoint method is a second-order method with two stages (see also the implicit midpoint method below): WebbAs always, we start with the simplest meaningful mathematical model, which for oscillations is a second-order differential equation: u ″ (t) + ω2u(t) = 0, where ω is a given physical parameter. Equation (4.40) models a one-dimensional system oscillating without damping (i.e., with negligible damping).

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