TimeSteppers::RungeKutta::ButcherTableau Struct Reference

Public Attributes
std::vector< double >	substep_times
std::vector< std::vector< double > >	substep_coefficients
std::vector< double >	result_coefficients
std::vector< double >	error_coefficients
std::vector< std::vector< double > >	dense_coefficients

Member Data Documentation

dense_coefficients

std::vector<std::vector<double> > TimeSteppers::RungeKutta::ButcherTableau::dense_coefficients

Coefficient polynomials for dense output. Each entry is the coefficients of a polynomial that will be evaluated with the fraction of the way through the step at which output is desired:

$$\begin{array}{}\text{(1)}& y=y_0+\sum _i{y}_i^{\prime }\sum _j{p}_{ij}{x}^{j}0\le x\le 1\end{array}$$

The derivative at the start of the next step is available as an additional substep after the final real substep. Trailing zero polynomials can be omitted.

error_coefficients

std::vector<double> TimeSteppers::RungeKutta::ButcherTableau::error_coefficients

The coefficients for an error estimate. Often called $b^{\ast }$ or $\hat{b}$ in the literature. This is assumed to be one order less accurate than the main method.

result_coefficients

std::vector<double> TimeSteppers::RungeKutta::ButcherTableau::result_coefficients

The coefficients for the final result. Often called $b$ in the literature.

If the number of coefficients is smaller than the number of substeps defined in substep_coefficients, the extra substeps will only be performed when an error estimate is requested.

substep_coefficients

std::vector<std::vector<double> > TimeSteppers::RungeKutta::ButcherTableau::substep_coefficients

The coefficient matrix of the substeps. Do not include the initial empty row or the coefficients for the full step. Often called $A$ in the literature.

substep_times

std::vector<double> TimeSteppers::RungeKutta::ButcherTableau::substep_times

The times of the substeps, excluding the initial time step. Often called $c$ in the literature.

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The documentation for this struct was generated from the following file:

• src/Time/TimeSteppers/RungeKutta.hpp