petsc-3.7.1 2016-05-15
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# TSTHETA

DAE solver using the implicit Theta method Many br

### Options Database

| -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

### Notes

     -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
      -------------
            |  1

Many br

For the default Theta=0.5, this is also known as the implicit midpoint rule. Many br

### When the endpoint variant is chosen, the method becomes a 2-stage method with first stage explicit

      0 | 0         0
      1 | 1-Theta   Theta
      -------------------
        | 1-Theta   Theta

Many 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

### See Also

TSCreate(), TS, TSSetType(), TSCN, TSBEULER, TSThetaSetTheta(), TSThetaSetEndpoint()

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

### Examples

src/ts/examples/tutorials/ex10.c.html
src/ts/examples/tutorials/ex14.c.html
src/ts/examples/tutorials/ex17.c.html
src/ts/examples/tutorials/ex31.c.html