3 papers
math.NA2025
Explicit Runge-Kutta-Chebyshev methods of second order with monotonic stability polynomial
Boris Faleichik, Andrew Moisa
A new Chebyshev-type family of stabilized explicit methods for solving mildly stiff ODEs is presented. Besides conventional conditions of order and stability we impose an additiona…
math.NA2020
Stabilized explicit Adams-type methods
Vasily Repnikov, Boris Faleichik, Andrey Moysa
In this work we present explicit Adams-type multistep methods with extended stability interval, which are analogous to the stabilized Chebyshev Runge--Kutta methods. It is proved t…
math.NA2019
Minimal residual multistep methods for large stiff non-autonomous linear problems
Boris Faleichik
The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form…