-ts_theta_theta <Theta> | - Location of stage (0<Theta<=1) Many br | |
-ts_theta_endpoint <flag> | - Use the endpoint (like Crank-Nicholson) instead of midpoint form of the Theta method Many br | |
-ts_theta_adapt <flg> | - Use time-step adaptivity with the Theta method Many br | |
-ts_theta_initial_guess_extrapolate <flg> | - Extrapolate stage initial guess from previous solution (sometimes unstable) Many br |
-ts_type theta -ts_theta_theta 1.0 corresponds to backward Euler (TSBEULER)
-ts_type theta -ts_theta_theta 0.5 corresponds to the implicit midpoint rule
-ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN)
This method can be applied to DAE. Many br
This method is cast as a 1-stage implicit Runge-Kutta method. Many br
Theta | Theta ------------- | 1Many br
For the default Theta=0.5, this is also known as the implicit midpoint rule. Many br
0 | 0 0 1 | 1-Theta Theta ------------------- | 1-Theta ThetaMany br
For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN). Many br
To apply a diagonally implicit RK method to DAE, the stage formula Many br
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 values (Y'_j, j<i) Many br
Level:beginner
Location:src/ts/impls/implicit/theta/theta.c
Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages