Class ode_it_solve (o2scl)¶

O2scl : Class List

template<class func_t = ode_it_funct, class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>, class matrix_row_t = boost::numeric::ublas::matrix_row<boost::numeric::ublas::matrix<double>>, class solver_vec_t = boost::numeric::ublas::vector<double>, class solver_mat_t = boost::numeric::ublas::matrix<double>> class ode_it_solve¶

ODE solver using a generic linear solver to solve finite-difference equations.

Idea for Future:

Set up convergence error if it goes beyond max iterations

Create a GSL-like set() and iterate() interface

Implement as a child of ode_bv_solve ?

Max and average tolerance?

Allow the user to ensure that the solver doesn’t apply the full correction

Storage for functions

func_t *fl¶

func_t *fr¶

func_t *fd¶

o2scl_linalg::linear_solver<solver_vec_t, solver_mat_t> *solver¶: Solver.

inline virtual double fd_left(size_t ieq, size_t ivar, double x, matrix_row_t &y)¶

Compute the derivatives of the LHS boundary conditions.

This function computes \( \partial f_{left,\mathrm{ieq}} / \partial y_{\mathrm{ivar}} \)

inline virtual double fd_right(size_t ieq, size_t ivar, double x, matrix_row_t &y)¶

Compute the derivatives of the RHS boundary conditions.

This function computes \( \partial f_{right,\mathrm{ieq}} / \partial y_{\mathrm{ivar}} \)

inline virtual double fd_derivs(size_t ieq, size_t ivar, double x, matrix_row_t &y)¶

Compute the finite-differenced part of the differential equations.

This function computes \( \partial f_{\mathrm{ieq}} / \partial y_{\mathrm{ivar}} \)

Public Functions

inline ode_it_solve()¶

inline virtual ~ode_it_solve()¶

inline int set_solver(o2scl_linalg::linear_solver<solver_vec_t, solver_mat_t> &ls)¶: Set the linear solver.

inline int solve(size_t n_grid, size_t n_eq, size_t nb_left, vec_t &x, mat_t &y, func_t &derivs, func_t &left, func_t &right, solver_mat_t &mat, solver_vec_t &rhs, solver_vec_t &dy)¶

Solve derivs with boundary conditions left and right.

Given a grid of size n_grid and n_eq differential equations, solve them by relaxation. The grid is specified in x, which is a vector of size n_grid. The differential equations are given in derivs, the boundary conditions on the left hand side in left, and the boundary conditions on the right hand side in right. The number of boundary conditions on the left hand side is nb_left, and the number of boundary conditions on the right hand side should be n_eq-nb_left. The initial guess for the solution, a matrix of size [n_grid][n_eq] should be given in y. Upon success, y will contain an approximate solution of the differential equations. The matrix mat is workspace of size [n_grid*n_eq][n_grid*n_eq], and the vectors rhs and y are workspace of size [n_grid*n_eq].

template<class dfunc_t> inline int solve_derivs(size_t n_grid, size_t n_eq, size_t nb_left, vec_t &x, mat_t &y, func_t &derivs, func_t &left, func_t &right, dfunc_t &d_derivs, dfunc_t &d_left, dfunc_t &d_right, solver_mat_t &mat, solver_vec_t &rhs, solver_vec_t &dy)¶

Solve derivs with boundary conditions left and right.

Public Members

bool make_mats¶

int verbose¶: Set level of output (default 0)

double eps_rel¶: Stepsize for finite differencing (default \( 10^{-4} \))

double eps_min¶: Minimum stepsize for finite differencing (default \( 10^{-15} \))

double tol_rel¶: Tolerance (default \( 10^{-8} \))

size_t niter¶: Maximum number of iterations (default 30)

double alpha¶: Size of correction to apply (default 1.0)

o2scl_linalg::linear_solver_HH<solver_vec_t, solver_mat_t> def_solver¶: Default linear solver.