Explicit Runge-Kutta-Chebyshev methods of second order with monotonic stability polynomial

2025/04/01 by Boris Faleichik, Faleichik, Boris, Andrew Moisa +1
Mathematics · #65L04 #65L05 #65L06 #65L20 #65M20 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2504.00323

openalex publication_date 2025/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 additional restriction on the methods: their stability function must be monotonically increasing and positive along the largest possible interval of negative real axis. Although stability intervals of the proposed methods are smaller than those of classic Chebyshev-type methods, their stability functions are more consistent with the exponent, they have more convex stability regions and smaller error constants. These properties allow the monotonic methods to be competitive with contemporary stabilized second-order methods, as the presented results of numerical experiments demonstrate.

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