in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

In this paper a new class of proximal-like algorithms for solving monotone inclusions of the form T (x) 3 0 is derived. It is obtained by applying linear multi-step methods (LMM) of numerical integration in order to solve the differential inclusion ẋ(t) ∈ −T (x(t)), which can be viewed as a generalization of the steepest decent method for a convex function. It is proved that under suitable cond...

In this paper the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their Lp-consistency, numerical Lp-stability and Lpconvergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-squa...

We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. Previously, we considered Maruyama-type schemes, where only the increments of the driving Wiene...