Geodesic
Stabilised explicit Adams-type methods
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2021), pp. 82-98

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In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any $k \geq 1$ 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 the general case, to construct a $k$-step method of order $p$ it is necessary to solve a constrained optimisation 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.
Keywords: numerical ODE solution; stiffness; stability interval; absolute stability; multi-step methods; Adams-type methods; explicit methods. 
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     author = {V. I. Repnikov and B. V. Faleichik and A. V. Moisa},
     title = {Stabilised explicit {Adams-type} methods},
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     pages = {82--98},
     publisher = {mathdoc},
     volume = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a7/}
}
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V. I. Repnikov; B. V. Faleichik; A. V. Moisa. Stabilised explicit Adams-type methods. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2021), pp. 82-98. http://geodesic.mathdoc.fr/item/BGUMI_2021_2_a7/