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Author:Dmitriy B. Berg , T. E. Simos
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (8), pp.1521-1547Springer
Abstract:It is of twelfth algebraic order.
Author:Dmitriy B. Berg , T. E. Simos
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (5), pp.1213-1235Springer
Abstract:For the first time in the literature we develop in this paper a three stages symmetric six-step scheme with twelfth algebraic and eliminated phase-lag and its first derivative. An additional characteristic of the new scheme is that the first and the second layer denote the a...
Author:Lan Yang , T. E. Simos
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (9), pp.1755-1778Springer
Abstract:A new scheme is developed in this paper, for the first time in the literature. The new scheme: (1) is a symmetric two-step method, (2) is of three-stages scheme, (3) is a high order method (i.e of eight-algebraic order), (4) the approximations of the layers are taken place a...
Author:Jing Ma , T. E. Simos
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (8), pp.1649-1668Springer
Abstract:An efficient and computational effective algorithm is introduced, for the first time in the literature, in the present paper. The main properties of the scheme are: (1) the algorithm is a two-step scheme, (2) the algorithm is symmetric one, (3) it is a hight algebraic order ...
Author:Ch. Tsitouras , T. E. Simos
Data Source:[J].Mediterranean Journal of Mathematics(IF 0.641), 2018, Vol.15 (2), pp.1-17Springer
Abstract:Abstract(#br)A new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods is presented for the solution of some special second order Initial Value Problem. After dealing with a reduced set of order conditions, we derive an optimal constant coefficient...
Author:Ch. Tsitouras , T. E. Simos
Data Source:[J].Mediterranean Journal of Mathematics(IF 0.641), 2018, Vol.15 (4), pp.1-16Springer
Abstract:Abstract(#br)An effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for the solution of the special second-order initial value problem. The new method uses variable step, is trigonometric fitted and the phase-lag is nullified along with its first...
Author:T. Monovasilis , Z. Kalogiratou , T. E. Simos
Data Source:[J].Mediterranean Journal of Mathematics(IF 0.641), 2016, Vol.13 (4), pp.2271-2285Springer
Abstract:Abstract(#br)In this work, we give the general framework for constructing trigonometrically fitted symplectic Runge–Kutta–Nyström (RKN) methods from symplectic trigonometrically fitted partitioned Runge–Kutta (PRK) methods. We construct RKN methods from PRK methods with...
Author:Wei Zhang , T. E. Simos
Data Source:[J].Mediterranean Journal of Mathematics(IF 0.641), 2016, Vol.13 (6), pp.5177-5194Springer
Abstract:Abstract(#br)In this paper, we will develop a four-stage high algebraic order symmetric two-step method with vanished phase-lag and its first up to the fourth derivative. For the proposed method, we will study the following: the phase-lag analysis of the new method; the deve...
Author:Ibraheem Alolyan , T. E. Simos
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (1), pp.105-131Springer
Abstract:Abstract(#br)The presentation, development and analysis of a new two-stages tenth algebraic order symmetric six-step method is introduced, for the first time in the literature, in this paper. More specifically, we present the development of the new method (requesting the hig...
Author:Jianbin Zhao , T. E. Simos
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (3), pp.697-716Springer
Abstract:Abstract(#br)In the present paper we will develop and analyse a new five-stages symmetric two-step method of high algebraic order with vanished phase-lag and its first, second, third, fourth and fifth derivatives. We will construct the new method. We will compute its local l...

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