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SpECTRE
v2024.04.12
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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 |
| 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{equation} y = y_0 + \sum_i y'_i \sum_j p_{ij} x^j \qquad 0 \le x \le 1 \end{equation}
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.
| std::vector<double> TimeSteppers::RungeKutta::ButcherTableau::error_coefficients |
The coefficients for an error estimate. Often called \(b^*\) or \(\hat{b}\) in the literature.
| 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.
| 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.
| std::vector<double> TimeSteppers::RungeKutta::ButcherTableau::substep_times |
The times of the substeps, excluding the initial time step. Often called \(c\) in the literature.