This method is cast as a 1-stage implicit Runge-Kutta method.
Theta | Theta ------------- | 1
For the default Theta=0.5, this is also known as the implicit midpoint rule.
0 | 0 0 1 | 1-Theta Theta ------------------- | 1-Theta Theta
For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN).
To apply a diagonally implicit RK method to DAE, the stage formula
Y_i = X + h sum_j a_ij Y'_j
is interpreted as a formula for Y'_i in terms of Y_i and known stuff (Y'_j, j<i)
Index of all TS routines
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Index of all manual pages