Algebraic-based nonstandard time-stepping schemes
For researchers in numerical methods, this preliminary work proposes a novel approach to time-stepping that offers internal filtering properties, though results are incremental and lack concrete performance metrics.
This work introduces nonstandard time-stepping schemes for solving differential equations by replacing finite difference derivative approximations with algebraic estimation, demonstrating improved slope predictions in RK-based methods.
In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of "internal" filtering. We consider firstly a classical finite difference method, like the explicit Euler method for which we study the possibility of using the algebraic estimation of derivatives instead of the usual finite difference to compute the numerical derivation. Then, we investigate how to use the algebraic estimation of derivatives in order to improve the slope predictions in RK-based schemes.