---
name: "continuation"
section: "4rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.0-2+b1"
release: "Debian 10 (Buster)"
platforms: ["linux"]
url: "https://new.carta.tech/continuation/4rheolef"
---

# continuation(4rheolef)

## NAME

**continuation** -- continuation algorithm for nonlinear problems

## DESCRIPTION

This function applies a continuation algorithm for the resolution of the following problem:

```
       F(lambda,u) = 0

```

where **lambda** is a parameter and **u** is the corresponding solution. The main idea is to follow a branch of solution **u(lambda)** when the parameter **lambda** varies. A simple call to the algorithm writes:

```
    my_problem P;
    field uh (Vh,0);
    continuation (P, uh, &dout, &derr);

```

The continuation algorithm bases on the **damped\_newton** (see damped\_newton(4)) and thus requirement for the **my\_problem** class may contains methods for the evaluation of F (aka the residue) and its derivative:

```
    class my_problem {
    public:
      typedef value_type;
      typedef float_type;
      string parameter_name() const;
      float_type parameter() const;
      void set_parameter (float_type lambda);
      value_type residue          (const value_type& uh) const;
      void update_derivative      (const value_type& uh) const;
      csr<float_type> derivative  (const value_type& uh) const;
      value_type derivative_versus_parameter (const field& uh) const;
      value_type derivative_solve      (const value_type& mrh) const;
      value_type derivative_trans_mult (const value_type& mrh) const;
      bool stop (const value_type& xh) const;
      idiststream& get (idiststream& is,       value_type& uh);
      odiststream& put (odiststream& os, const value_type& uh) const;
      float_type space_norm (const value_type& uh) const;
      float_type dual_space_norm (const value_type& mrh) const;
      float_type space_dot (const value_type& xh, const value_type& yh) const;
      float_type dual_space_dot (const value_type& mrh, const value_type& msh) const;
      value_type massify   (const value_type& uh) const;
      value_type unmassify (const value_type& mrh) const;
    };

```

See the example **combustion.h** in the user's documentation for more. The optional argument of type class **continuation\_option** (see continuation\_option(2)) allows one to control some features of the algorithm.

## IMPLEMENTATION

```
template<class Problem>
void
continuation (
  Problem&                        F,
  typename Problem::value_type&   uh,
  odiststream*                    p_out,
  odiststream*                    p_err,
  const continuation_option& opts = continuation_option())

```

## SEE ALSO

damped\_newton(4), continuation\_option(2)

## COPYRIGHT

Copyright (C) 2000-2018 Pierre Saramito \<Pierre.Saramito@imag.fr\> GPLv3+: GNU GPL version 3 or later \<http://gnu.org/licenses/gpl.html\>. This is free software: you are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by law.