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Journal articles on the topic 'Predictor-corrector method'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Adetola Olaide, Adesanya, M. R. Odekunle, and A. O. Adeyeye. "Continuous Block-Predictor Hybrid-Corrector Method." International Journal of Mathematics and Soft Computing 2, no. 2 (July 21, 2012): 35. http://dx.doi.org/10.26708/ijmsc.2012.2.2.05.

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2

JOSHI, MARK, and ALEXANDER WIGUNA. "ACCELERATING PATHWISE GREEKS IN THE LIBOR MARKET MODEL." International Journal of Theoretical and Applied Finance 15, no. 02 (March 2012): 1250012. http://dx.doi.org/10.1142/s0219024912500124.

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In the framework of the displaced-diffusion LIBOR market model, we derive the pathwise adjoint method for the iterative predictor-corrector and one of the Glasserman–Zhao drift approximations in the spot measure. This allows us to compute fast deltas and vegas under these schemes. We compare the discretisation bias obtained when computing Greeks with these methods to those obtained under the log-Euler and predictor-corrector approximations by performing tests with interest rate caplets and cancellable receiver swaps. The two predictor-corrector type methods were the most accurate by far. In particular, we found the iterative predictor-corrector method to be more accurate and slightly faster than the predictor-corrector method, the Glasserman–Zhao method, used, to be relatively fast but highly inconsistent, and the log-Euler method to be reasonably accurate but only at low volatilities. Standard errors were not significantly different across all four discretisations.

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3

Shang, Dequan, and Xiaobin Guo. "Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/312328.

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A predictor-corrector algorithm and an improved predictor-corrector (IPC) algorithm based on Adams method are proposed to solve first-order differential equations with fuzzy initial condition. These algorithms are generated by updating the Adams predictor-corrector method and their convergence is also analyzed. Finally, the proposed methods are illustrated by solving an example.

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4

Luo, Zhiquan, Shiquan Wu, and Yinyu Ye. "Predictor-corrector method for nonlinear complementarity problem." Acta Mathematicae Applicatae Sinica 13, no. 3 (July 1997): 321–28. http://dx.doi.org/10.1007/bf02025887.

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5

Inayat Noor, Khalida, and Muhammad Aslam Noor. "Predictor–corrector Halley method for nonlinear equations." Applied Mathematics and Computation 188, no. 2 (May 2007): 1587–91. http://dx.doi.org/10.1016/j.amc.2006.11.023.

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6

Oghonyon, J. G., S. A. Okunuga, K. S. Eke, and O. A. Odetunmibi. "Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations." Engineering, Technology & Applied Science Research 8, no. 3 (June 19, 2018): 2943–48. http://dx.doi.org/10.48084/etasr.1914.

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Block predictor-corrector method for solving non-stiff ordinary differential equations (ODEs) started with Milne’s device. Milne’s device is an extension of the block predictor-corrector method providing further benefits and better results. This study considers Milne’s devise for solving fourth order ODEs. A combination of Newton’s backward difference interpolation polynomial and numerical integration method are applied and integrated at some selected grid points to formulate the block predictor-corrector method. Moreover, Milne’s devise advances the computational efficiency by applying the principal local truncation error (PLTE) of the block predictor-corrector method after establishing the order. The numerical results were exhibited to attest the functioning of Milne’s devise in solving fourth order ODEs. The complete results were obtained with the aid of Mathematica 9 kernel for Microsoft Windows. Numerical results showcase that Milne’s device is more effective than existent methods in terms of design new step size, determining the convergence criteria and maximizing errors at all examined convergence levels.

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7

Balbo, Antonio Roberto, Márcio Augusto da Silva Souza, Edméa Cássia Baptista, and Leonardo Nepomuceno. "Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis." Mathematical Problems in Engineering 2012 (2012): 1–26. http://dx.doi.org/10.1155/2012/376546.

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This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures (IPLS) in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch (ED) problem studied in the field of power systems analysis. The theory of the method is examined for quadratic programming problems and involves the analysis of iterative schemes, computational implementation, and issues concerning the adaptation of the proposed algorithm to solve ED problems. Numerical results are presented, which demonstrate improvements and the efficiency of the IPLS method when compared to several other methods described in the literature. Finally, postoptimization analyses are performed for the solution of ED problems.

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8

Choi, Hong Won, Young Ju Choi, and Sang Kwon Chung. "A PREDICTOR-CORRECTOR METHOD FOR FRACTIONAL EVOLUTION EQUATIONS." Bulletin of the Korean Mathematical Society 53, no. 6 (November 30, 2016): 1725–39. http://dx.doi.org/10.4134/bkms.b150901.

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9

Kim, Jong Hoon, and Yong Hyup Kim. "A predictor–corrector method for structural nonlinear analysis." Computer Methods in Applied Mechanics and Engineering 191, no. 8-10 (December 2001): 959–74. http://dx.doi.org/10.1016/s0045-7825(01)00296-1.

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10

Bao, Zong-Ke, Ming Huang, and Xi-Qiang Xia. "A Predictor-Corrector Method for Solving Equilibrium Problems." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/313217.

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We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise toΔ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.

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11

Luo, Zhi-Quan, and Shiquan Wu. "A modified predictor-corrector method for linear programming." Computational Optimization and Applications 3, no. 1 (March 1994): 83–91. http://dx.doi.org/10.1007/bf01299392.

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12

Mehrotra, Sanjay. "Asymptotic convergence in a generalized predictor-corrector method." Mathematical Programming 74, no. 1 (July 1996): 11–28. http://dx.doi.org/10.1007/bf02592143.

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13

Yang, Chao, Duo Li, Tao Zhu, and Shoune Xiao. "Assessment of numerical integration algorithms for nonlinear vibration of railway vehicles." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 231, no. 6 (March 31, 2016): 729–39. http://dx.doi.org/10.1177/0954409716640825.

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The primary purpose of this paper was to choose appropriate time integration methods for the simulation of nonlinear railway vehicle systems. The nonlinear elements existing in railway vehicle systems were summarized, and the relevant mathematical expressions were provided. A newly developed integration method, which is the corrected explicit method of double time steps, was implemented in five typical nonlinear examples of nonlinear railway vehicle systems. The Newmark method, the Wilson-θ method, the Runge–Kutta method, the predictor-corrector Adams method, the Zhai method, and the precise integration method were also employed for comparison purpose. Finally, the scope of application of these methods was pointed out . The results show that the Newmark method and the Wilson-θ method should not be applied to nonlinear railway vehicle systems as these methods result in errors. In contrast to the predictor-corrector Adams method and the precise integration method, the Runge–Kutta method with error control (RK45) is not applicable to the non-smooth problems although the RK45 possesses high accuracy. In addition, the application of the RK45 and the predictor-corrector Adams method with error control may result in spurious tiny oscillation in the vehicle system related to nonlinear vertical wheel–rail forces. The corrected explicit method of double time steps, the Zhai method, the standard Runge–Kutta method, the precise integration method, the RK45, and the predictor-corrector Adams method which possess tight error tolerances are recommended for nonlinear railway vehicle systems according to the requirements of accuracy and computational efficiency.

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14

Zaitsev, V. V., and E. Yu Fedyunin. "THE PREDICTOR-CORRECTOR METHOD FOR MODELLING OF NONLINEAR OSCILLATORS." Vestnik of Samara University. Natural Science Series 25, no. 1 (September 6, 2019): 97. http://dx.doi.org/10.18287/2541-7525-2019-25-1-97-103.

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15

Carrington, David B., Xiuling Wang, and Darrell W. Pepper. "PREDICTOR-CORRECTOR SPLIT PROJECTION METHOD FOR TURBULENT REACTIVE FLOW." Computational Thermal Sciences 5, no. 4 (2013): 333–53. http://dx.doi.org/10.1615/computthermalscien.2013005819.

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16

WU, CAIYING, and GUOQING CHEN. "PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING." Bulletin of the Australian Mathematical Society 79, no. 3 (April 17, 2009): 367–76. http://dx.doi.org/10.1017/s0004972708001214.

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AbstractThere has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

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17

Yamamoto, Akio, Masahiro Tatsumi, and Naoki Sugimura. "Projected Predictor-Corrector Method for Lattice Physics Burnup Calculations." Nuclear Science and Engineering 163, no. 2 (October 2009): 144–51. http://dx.doi.org/10.13182/nse08-80.

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18

Sun, Jie, and Jishan Zhu. "A predictor-corrector method for extended linear-quadratic programming." Computers & Operations Research 23, no. 8 (August 1996): 755–67. http://dx.doi.org/10.1016/0305-0548(95)00076-3.

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19

Voss, D. A., and A. Q. M. Khaliq. "A sixth order predictor-corrector method for periodic IVPs." Applied Mathematics Letters 2, no. 1 (1989): 65–68. http://dx.doi.org/10.1016/0893-9659(89)90119-5.

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20

Simos, T. E. "A high order predictor-corrector method for periodic IVPS." Applied Mathematics Letters 6, no. 5 (September 1993): 9–12. http://dx.doi.org/10.1016/0893-9659(93)90090-a.

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21

Daftardar-Gejji, Varsha, Yogita Sukale, and Sachin Bhalekar. "A new predictor–corrector method for fractional differential equations." Applied Mathematics and Computation 244 (October 2014): 158–82. http://dx.doi.org/10.1016/j.amc.2014.06.097.

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22

Sagara, Nobuko, and Masao Fukushima. "An efficient predictor-corrector method for solving nonlinear equations." Journal of Computational and Applied Mathematics 19, no. 3 (September 1987): 343–49. http://dx.doi.org/10.1016/0377-0427(87)90203-2.

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23

Probst, Roy Wilhelm, and Aurelio Ribeiro Leite Oliveira. "A new predictor–corrector method for optimal power flow." Optimization and Engineering 16, no. 2 (October 7, 2014): 335–46. http://dx.doi.org/10.1007/s11081-014-9265-7.

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24

Liu, Yilin, Xuqiang Shao, and Zhaohui Wu. "Rotation Invariant Predictor-Corrector for Smoothed Particle Hydrodynamics Data Visualization." Symmetry 13, no. 3 (February 26, 2021): 382. http://dx.doi.org/10.3390/sym13030382.

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In order to extract the vortex features more accurately, a new method of vortex feature extraction on the Smoothed Particle Hydrodynamics data is proposed in the current study by combining rotation invariance and predictor-corrector method. There is a limitation in the original rotation invariance, which can only extract the vortex features that perform equal-speed rotations. The limitation is slightly weakened to a situation that the rotation invariance can be used, given that a specific axis is existed in the fluid to replace the axis needed for it. Therefore, as long as the axis exists, the modified rotation invariant method can be used. Meanwhile, the vortex features are extracted by predictor-corrector method. By calculating the cross product of the parallel vector field, the seed candidates of vortex core lines can be obtained, and the real seed points can be gained from the rotation invariant Jacobian. Finally, the seed point and a series of candidates based on the predictor-corrector method are connected to draw the vortex core lines. Compared with the original method, the rotation invariant predictor-corrector method not only expands the application scope, but also ensures the accuracy of extraction. Our method adds the steps of calculating the rotation invariant Jacobian, the performance is slightly lower, but with the increase of the particle number, the performance gradually tends to the original method.

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25

BRATSOS, A. G. "AN IMPROVED SECOND-ORDER NUMERICAL METHOD FOR THE GENERALIZED BURGERS–FISHER EQUATION." ANZIAM Journal 54, no. 3 (January 2013): 181–99. http://dx.doi.org/10.1017/s1446181113000138.

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AbstractA second-order in time finite-difference scheme using a modified predictor–corrector method is proposed for the numerical solution of the generalized Burgers–Fisher equation. The method introduced, which, in contrast to the classical predictor–corrector method is direct and uses updated values for the evaluation of the components of the unknown vector, is also analysed for stability. Its efficiency is tested for a single-kink wave by comparing experimental results with others selected from the available literature. Moreover, comparisons with the classical method and relevant analogous modified methods are given. Finally, the behaviour and physical meaning of the two-kink wave arising from the collision of two single-kink waves are examined.

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26

NEUBERT, R. "PREDICTOR-CORRECTOR TECHNIQUES FOR DETECTING HOPF BIFURCATION POINTS." International Journal of Bifurcation and Chaos 03, no. 05 (October 1993): 1311–18. http://dx.doi.org/10.1142/s0218127493001069.

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A new method for stability analysis during continuation is proposed. The method uses shifted inverse iteration to compute a relevant eigenvalue, determining stability. Some additional work has to be done to verify the above solution. Numerical experiments are performed using models of the tubular reactor and the Brusselator.

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27

BRUTI-LIBERATI, NICOLA, and ECKHARD PLATEN. "STRONG PREDICTOR–CORRECTOR EULER METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 08, no. 03 (September 2008): 561–81. http://dx.doi.org/10.1142/s0219493708002457.

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This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor–corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to overcome some of the numerical instabilities that are often experienced when using the explicit Euler method. This is of importance, for instance, in finance where martingale dynamics arise for solutions of SDEs with multiplicative diffusion coefficients. Numerical experiments demonstrate the improved asymptotic stability properties of the proposed symmetric predictor–corrector Euler methods.

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28

Ting, Yung, Tho Van Nguyen, and Jia-Ci Chen. "Design and performance evaluation of an exponentially weighted moving average–based adaptive control for piezo-driven motion platform." Advances in Mechanical Engineering 10, no. 6 (June 2018): 168781401876719. http://dx.doi.org/10.1177/1687814018767194.

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In this article, building a controlled system with velocity feedback in the inner loop for a platform driven by piezoelectric motors is investigated. Such a motion control system is subject to disturbance such as friction, preload, and temperature rise in operation. Especially, temperature rise is an essential problem of using piezoelectric motor, but very few research works address this topic in depth. Exponentially weighted moving average method has been widely used in process control to deal with systematic change and drift disturbance. It is attempted to map the exponentially weighted moving average method and the predictor corrector control with two exponentially weighted moving average formulas into a run-to-run model reference adaptive system for velocity control. Using a predictive friction model, a dead-zone compensator is built that can reduce the friction effect and provide an approximately linear relation of the input voltage and the output velocity for the subsequent exponentially weighted moving average or predictor corrector control control design. Comparison of the exponentially weighted moving average, predictor corrector control, and proportional–integral–derivative controllers is carried out in experiment with different speed patterns on a single-axis and a bi-axial platform. The results indicate that the proposed run-to-run-model reference adaptive system predictor corrector control is superior to the other methods.

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29

Torabi, Mina, Manuel Pastor, and Miguel Martín Stickle. "Three-step Predictor-Corrector Finite Element Schemes for Consolidation Equation." Mathematical Problems in Engineering 2020 (April 28, 2020): 1–14. http://dx.doi.org/10.1155/2020/2873869.

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An accurate, stable, and efficient three-step predictor-corrector time integration method is considered, for the first time, to obtain numerical solution for the one-dimensional consolidation equation within a finite and spectral element framework. Theoretical order of accuracy and stability conditions are provided. The three-step predictor-corrector time integration method is third-order accurate and shows a larger stability region than the forward Euler method when applied to the one-dimensional consolidation equation. Furthermore, numerical results are in agreement with analytical solutions previously derived by the authors.

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30

Nayak, R. K., M. P. Biswal, and S. Padhy. "An Implementable Predictor-Corrector Method for Solving Semidefinite Programming Problems." Journal of Interdisciplinary Mathematics 17, no. 3 (May 4, 2014): 223–42. http://dx.doi.org/10.1080/09720502.2013.821780.

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31

Voss, D. A., and A. Q. M. Khaliq. "A linearly implicit predictor-corrector method for reaction-diffusion equations." Computers & Mathematics with Applications 38, no. 11-12 (December 1999): 207–16. http://dx.doi.org/10.1016/s0898-1221(99)00299-0.

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32

Wang, Peng, Dong Zuo, Fang Yang, Liyan Wang, and Dongliang Sun. "Performance conversion of centrifugal compressors based on predictor corrector method." Chinese Science Bulletin 63, no. 5-6 (February 1, 2018): 571–78. http://dx.doi.org/10.1360/n972017-01120.

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33

Chen, Yongrong, and Chongchao Huang. "Predictor-Corrector Smoothing Method for the Asymmetric Traffic Equilibrium Problem." Advanced Science Letters 7, no. 1 (March 30, 2012): 622–25. http://dx.doi.org/10.1166/asl.2012.2678.

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34

Aslam Noor, Muhammad, Khalida Inayat Noor, and Saira Zainab. "On a predictor–corrector method for solving invex equilibrium problems." Nonlinear Analysis: Theory, Methods & Applications 71, no. 7-8 (October 2009): 3333–38. http://dx.doi.org/10.1016/j.na.2009.01.235.

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35

Ma, Yun-Jie. "Reconstruction of a Robin Coefficient by a Predictor-Corrector Method." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/496587.

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The present paper is devoted to solving a nonlinear inverse problem of identifying a Robin coefficient from boundary temperature measurement. A numerical algorithm on the basis of the predictor-corrector method is designed to restore the approximate solution and the performance of the method is verified by simulating several examples. The convergence with respect to the amount of noise in the data is also investigated.

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36

Zhang, Bin, Jiang Hang Wang, Hong Liu, and Fang Chen. "The Predictor-Corrector Method for One-Dimensional Stiff Detonation Capturing." Advanced Materials Research 717 (July 2013): 415–20. http://dx.doi.org/10.4028/www.scientific.net/amr.717.415.

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A new fractional step method is proposed for stiff chemical reactive flows. In stiff reaction problems, wrong propagation speed of detonation wave may occur in general fraction step algorithm. During the reaction step, the proposed scheme replaces the average representation with two-reconstruction values which are obtained by predictor-corrector steps. For numerical experiments, the first-order upwind AUSM scheme and the explicit Euler method are considered. Several one-dimensional stiff reactive flows are investigated. The numerical results show that the propagation speed of the detonation wave computed by the standard method is faster than the exact solution. However, the numerical solutions by the proposed method have very good agreement with the exact solution.

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37

Preda, Vasile, Miruna Beldiman, and Anton BaÌtaÌtorescu. "A predictor-corrector method for a class of equilibrium problems." PAMM 7, no. 1 (December 2007): 2060023–24. http://dx.doi.org/10.1002/pamm.200700309.

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38

Kroes, G. J. "The royal road to an energy-conserving predictor-corrector method." Computer Physics Communications 70, no. 1 (May 1992): 41–52. http://dx.doi.org/10.1016/0010-4655(92)90089-h.

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39

Syam, Muhammed I. "Conjugate gradient predictor corrector method for solving large scale problems." Mathematics of Computation 74, no. 250 (September 16, 2004): 805–19. http://dx.doi.org/10.1090/s0025-5718-04-01689-8.

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40

Riazy, S., T. Wendler, and J. Pilz. "Automatic two-channel sleep staging using a predictor–corrector method." Physiological Measurement 39, no. 1 (January 31, 2018): 014006. http://dx.doi.org/10.1088/1361-6579/aaa109.

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41

Zhang, Ju-liang, and Jian Chen. "A New Noninterior Predictor–Corrector Method for the P0 LCP." Applied Mathematics and Optimization 53, no. 1 (October 25, 2005): 79–100. http://dx.doi.org/10.1007/s00245-005-0836-z.

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42

Rezaiee-Pajand, Mohammad, and Mahdi Karimi-Rad. "An accurate predictor-corrector time integration method for structural dynamics." International Journal of Steel Structures 17, no. 3 (September 2017): 1033–47. http://dx.doi.org/10.1007/s13296-017-9014-9.

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43

Karamyshev, V. B., and V. M. Kovenya. "The predictor-corrector method for solving problems of gas dynamics." USSR Computational Mathematics and Mathematical Physics 28, no. 6 (January 1988): 188–94. http://dx.doi.org/10.1016/0041-5553(88)90063-8.

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44

Allahviranloo, T., N. Ahmady, and E. Ahmady. "Numerical solution of fuzzy differential equations by predictor–corrector method." Information Sciences 177, no. 7 (April 2007): 1633–47. http://dx.doi.org/10.1016/j.ins.2006.09.015.

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45

Allahviranloo, T., S. Abbasbandy, N. Ahmady, and E. Ahmady. "Improved predictor–corrector method for solving fuzzy initial value problems." Information Sciences 179, no. 7 (March 2009): 945–55. http://dx.doi.org/10.1016/j.ins.2008.11.030.

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46

Sagara, Nobuko, and Masao Fukushima. "A new predictor–corrector method for solving unconstrained minimization problems." Journal of Computational and Applied Mathematics 16, no. 3 (November 1986): 343–54. http://dx.doi.org/10.1016/0377-0427(86)90005-1.

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47

Noor, Muhammad Aslam. "A new predictor-corrector method for noncoercive mixed variational inequalities." Korean Journal of Computational & Applied Mathematics 7, no. 2 (May 2000): 363–71. http://dx.doi.org/10.1007/bf03012198.

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48

Zhang, Xiangsong, Sanyang Liu, and Zhenhua Liu. "A predictor-corrector smoothing method for second-order cone programming." Journal of Applied Mathematics and Computing 32, no. 2 (February 25, 2009): 369–81. http://dx.doi.org/10.1007/s12190-009-0256-3.

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49

Liu, Q. X., X. S. He, J. K. Liu, Y. M. Chen, and L. C. Huang. "Solving Fractional Dynamical System with Freeplay by Combining Memory-Free Approach and Precise Integration Method." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/9430528.

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The Yuan-Agrawal (YA) memory-free approach is employed to study fractional dynamical systems with freeplay nonlinearities subjected to a harmonic excitation, by combining it with the precise integration method (PIM). By the YA method, the original equations are transformed into a set of first-order piecewise-linear ordinary differential equations (ODEs). These ODEs are further separated as three linear inhomogeneous subsystems, which are solved by PIM together with a predictor-corrector process. Numerical examples show that the results by the presented method agree well with the solutions obtained by the Runge-Kutta method and a modified fractional predictor-corrector algorithm. More importantly, the presented method has higher computational efficiency.

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50

PANOPOULOS, G. A., Z. A. ANASTASSI, and T. E. SIMOS. "A NEW SYMMETRIC EIGHT-STEP PREDICTOR-CORRECTOR METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION AND RELATED ORBITAL PROBLEMS." International Journal of Modern Physics C 22, no. 02 (February 2011): 133–53. http://dx.doi.org/10.1142/s0129183111016154.

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A new general multistep predictor-corrector (PC) pair form is introduced for the numerical integration of second-order initial-value problems. Using this form, a new symmetric eight-step predictor-corrector method with minimal phase-lag and algebraic order ten is also constructed. The new method is based on the multistep symmetric method of Quinlan–Tremaine,1 with eight steps and 8th algebraic order and is constructed to solve numerically the radial time-independent Schrödinger equation. It can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with minimal phase-lag is the most efficient of all the compared methods and for all the problems solved.

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