The authors introduce Explicit and Effectively Symmetric (EES) Runge-Kutta schemes by minimizing the antisymmetric component of B-series methods via new order conditions, yielding explicit methods with near-symmetric properties that outperform standard explicit schemes in tests.
Springer Series in Computational Mathematics, vol
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The paper proves that Φ^CSRK has full row rank under the standard consistency condition for every consistent polynomial continuous-stage Runge-Kutta method.
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A polynomial moment approach to a rank condition for continuous-stage Runge--Kutta methods
The paper proves that Φ^CSRK has full row rank under the standard consistency condition for every consistent polynomial continuous-stage Runge-Kutta method.