in this paper, we present a new two-step trigonometrically fitted symmetric obrechkoff method. the method is based on the symmetric two-step obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve ivps with periodic solutions such as orbital problems. we compare the new method to some recently constructed optimized methods from the literature. the numeri...

The known proofs of the inverse theorems theory approximation by trigonometric polynomials and functions exponential type are based on idea S. N. Bernstein to expand a function in series containing its best approximation. In this paper, new method establish is introduced. We simple identities that immediately imply mentioned and, moreover, with better constants. This can be applied derivatives ...