# TSSetIJacobian#

Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function provided with `TSSetIFunction()`

.

## Synopsis#

```
#include "petscts.h"
PetscErrorCode TSSetIJacobian(TS ts, Mat Amat, Mat Pmat, TSIJacobian f, void *ctx)
```

Logically Collective

## Input Parameters#

## Calling sequence of f#

time at step/stage being solved**t -**state vector**U -**time derivative of state vector**U_t -**shift**a -**(approximate) Jacobian of F(t,U,W+a**Amat -***U), equivalent to dF/dU + a*dF/dU_tmatrix used for constructing preconditioner, usually the same as Amat**Pmat -**[optional] user-defined context for matrix evaluation routine**ctx -**

## Notes#

The matrices Amat and Pmat are exactly the matrices that are used by `SNES`

for the nonlinear solve.

If you know the operator Amat has a null space you can use `MatSetNullSpace()`

and `MatSetTransposeNullSpace()`

to supply the null
space to Amat and the `KSP`

solvers will automatically use that null space as needed during the solution process.

The matrix dF/dU + a*dF/dU_t you provide turns out to be
the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
The time integrator internally approximates U_t by W+a*U where the positive “shift”
a and vector W depend on the integration method, step size, and past states. For example with
the backward Euler method a = 1/dt and W = -a*U(previous timestep) so
W + a*U = a*(U - U(previous timestep)) = (U - U(previous timestep))/dt

You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f() You should not assume the values are the same in the next call to f() as you set them in the previous call.

## See Also#

TS: Scalable ODE and DAE Solvers, `TS`

, `TSSetIFunction()`

, `TSSetRHSJacobian()`

, `SNESComputeJacobianDefaultColor()`

, `SNESComputeJacobianDefault()`

, `TSSetRHSFunction()`

## Level#

beginner

## Location#

## Examples#

src/ts/tutorials/ex10.c.html

src/ts/tutorials/ex14.c.html

src/ts/tutorials/ex15.c.html

src/ts/tutorials/ex16.c.html

src/ts/tutorials/ex17.c.html

src/ts/tutorials/ex19.c.html

src/ts/tutorials/ex20adj.c.html

src/ts/tutorials/ex20.c.html

src/ts/tutorials/ex20fwd.c.html

src/ts/tutorials/ex20opt_ic.c.html

src/ts/tutorials/ex20opt_p.c.html

Index of all TS routines

Table of Contents for all manual pages

Index of all manual pages