Algorithm 1.

Combining model equations and numerical integration method description to yield abstract code. Here, the differential equations in vector form are dx/dt = f(x, t) where x is the vector of state variables with components x_v for variable v, and f is a vector function with corresponding components f_v. All statements in the numerical integration method should be understood as referring to vectors of variables and vector functions.

for all statements σ in the numerical integration method do

Expand f$(\underset{\_}{\widehat{x}},\underset{\_}{\widehat{t}})$ in σ

Replace xnew in σ by y

for all state variables v do

Append component σv of the transformed σ to code

end for

end for

for all state variables v do

Append xv = yv to code

end for