*Last updated: 2023-03-16.*

# tf_quant_finance.math.pde.steppers.implicit.implicit_step

View source Creates a stepper function with implicit time marching scheme. ```python tf_quant_finance.math.pde.steppers.implicit.implicit_step() ``` Given a space-discretized equation ``` du/dt = A(t) u(t) + b(t) ``` (here `u` is a value vector, `A` and `b` are the matrix and the vector defined by the PDE), the implicit time marching scheme approximates the right-hand side with its value after the time step: ``` (u(t2) - u(t1)) / (t2 - t1) = A(t2) u(t2) + b(t2) ``` This scheme is stable, but is only first order accurate. Usually, Crank-Nicolson or Extrapolation schemes are preferable. More details can be found in `weighted_implicit_explicit.py` describing the weighted implicit-explicit scheme - implicit scheme is a special case with `theta = 0`. #### Returns: Callable to be used in finite-difference PDE solvers (see fd_solvers.py).