Stabilised explicit Adams-type methods

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 ≥ 1 there exists an k-step method of order one interval length 2k. The first have remarkably simple expressions their coefficients and error constant. A damped modification these derived. general case, construct a p it necessary solve constrained optimisation problem in objective function constraints second degree polynomials variables. We calculate higher-order up six numerically perform some numerical experiments confirm accuracy