2020/12/12 by В. И. Репников, Repnikov, Vasily, Boris Faleichik +3
Computer Science · Mathematics · #65L04 #65L05 #65L06 #FOS: Mathematics #G.1.7 #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2012.06767
openalex publication_date 2020/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 that for any k≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In general case to construct a k-step method of order p it is necessary to solve a constrained optimization problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.