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...

All of the numerical methods that we have developed for solving initial value problems are onestep methods, because they only use information about the solution at time tn to approximate the solution at time tn+1. As n increases, that means that there are additional values of the solution, at previous times, that could be helpful, but are unused. Multistep methods are time-stepping methods that...

a new two-step implicit linear obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. the purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial schrodinger equation and related problems. this algorithm belongs in the category of the multist...

in this paper, we introduce the new class of implicit l-stable generalized hybrid methods forthe numerical solution of first order initial value problems. we generalize the hybrid methodswith utilize ynv directly in the right hand side of classical hybrid methods. the numericalexperimentation showed that our method is considerably more efficient compared to wellknown methods used for the numer...

page 1 Linear Multistep Methods Note: The authoritative reference for the material on convergence is the book by Peter Henrici, Discrete Variable Methods in Ordinary Differential Equations , Wiley, 1962. The best reference on absolute stability is the book by Jack Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, 1991. We consider the Initial Value Problem (IVP) y′ = f(x, y),...