Search results for: solving Sudoku puzzles
525 Application of Higher Order Splines for Boundary Value Problems
Authors: Pankaj Kumar Srivastava
Abstract:
Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have been included.Keywords: Septic spline, Octic spline, Nonic spline, Tenth, Eleventh, Twelfth and Thirteenth Degree spline, parametric and non-parametric splines, thermal instability, astrophysics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2770524 Combustion Analysis of Suspended Sodium Droplet
Authors: T. Watanabe
Abstract:
Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.
Keywords: Combustion, analysis, sodium, droplet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 699523 The Multi-scenario Knapsack Problem: An Adaptive Search Algorithm
Authors: Mhand Hifi, Hedi Mhalla, Mustapha Michaphy
Abstract:
In this paper, we study the multi-scenario knapsack problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of an adaptive algorithm for solving heuristically the problem. The used method combines two complementary phases: a size reduction phase and a dynamic 2- opt procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for reducing the size problem. Second, the adaptive search procedure is applied in order to attain a feasible solution Finally, the performances of two versions of the proposed algorithm are evaluated on a set of randomly generated instances.
Keywords: combinatorial optimization, max-min optimization, knapsack, heuristics, problem reduction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1621522 Review Risk and Threats Due to Dam Break
Authors: A.Roshandel, N.Hedayat, H.kiamanesh
Abstract:
The one of most important objects in implementation of damage analysis observations is manner of dam break wave propagation. In this paper velocity and wave height due dam break in with and without tailwater states for appointment hazardous lands and flood radius are investigate. In order to modeling above phenomenon finite volume method of Roe type for solving shallow water equations is used. Results indicated that in the dry bed state risk radius due to dam break is too high. While in the wet bed risk radius has a less wide. Therefore in the first state constructions and storage facilities are encountered with destruction risk. Further velocity due to dam break in the second state is more comparing to the first state. Hence erosion and scour the river bed in the dry bed is too more compare to the wet bed.Keywords: Dam break, finite volume method, tailwater, risk radius, scour
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1623521 Hardware Approach to Solving Password Exposure Problem through Keyboard Sniff
Authors: Kyungroul Lee, Kwangjin Bae, Kangbin Yim
Abstract:
This paper introduces a hardware solution to password exposure problem caused by direct accesses to the keyboard hardware interfaces through which a possible attacker is able to grab user-s password even where existing countermeasures are deployed. Several researches have proposed reasonable software based solutions to the problem for years. However, recently introduced hardware vulnerability problems have neutralized the software approaches and yet proposed any effective software solution to the vulnerability. Hardware approach in this paper is expected as the only solution to the vulnerabilityKeywords: Keyboard sniff, password exposure, hardware vulnerability, privacy problem, insider security.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1579520 Examining the Performance of Three Multiobjective Evolutionary Algorithms Based on Benchmarking Problems
Authors: Konstantinos Metaxiotis, Konstantinos Liagkouras
Abstract:
The objective of this study is to examine the performance of three well-known multiobjective evolutionary algorithms for solving optimization problems. The first algorithm is the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), the second one is the Strength Pareto Evolutionary Algorithm 2 (SPEA-2), and the third one is the Multiobjective Evolutionary Algorithms based on decomposition (MOEA/D). The examined multiobjective algorithms are analyzed and tested on the ZDT set of test functions by three performance metrics. The results indicate that the NSGA-II performs better than the other two algorithms based on three performance metrics.
Keywords: MOEAs, Multiobjective optimization, ZDT test functions, performance metrics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 952519 Attentiveness of Building Commissioning in the Malaysian Construction Industry
Authors: Kho Mei Ye, Hamzah Abdul Rahman
Abstract:
This paper provides some thoughts about the lack of attentiveness of building commissioning in the construction industry and the lack of handling in project commissioning as an integral part of the project life-cycle. Many have perceived commissioning as the problem solving process of a project, rather than the start up of the equipment, or the handing over of the project to the client. Therefore, there is a lack of proper attention in the planning of commissioning as a vital part of the project life-cycle. This review paper aims to highlight the benefits of building commissioning and to propose the lacking of knowledge gap on building commissioning. Finally, this paper hopes to propose the shift of focus on this matter in future research.Keywords: building, commissioning, construction, delay
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2156518 Transmission Lines Loading Enhancement Using ADPSO Approach
Authors: M. Mahdavi, H. Monsef, A. Bagheri
Abstract:
Discrete particle swarm optimization (DPSO) is a powerful stochastic evolutionary algorithm that is used to solve the large-scale, discrete and nonlinear optimization problems. However, it has been observed that standard DPSO algorithm has premature convergence when solving a complex optimization problem like transmission expansion planning (TEP). To resolve this problem an advanced discrete particle swarm optimization (ADPSO) is proposed in this paper. The simulation result shows that optimization of lines loading in transmission expansion planning with ADPSO is better than DPSO from precision view point.Keywords: ADPSO, TEP problem, Lines loading optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1620517 Solution of First kind Fredholm Integral Equation by Sinc Function
Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,
Abstract:
Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2758516 Response of the Residential Building Structureon Load Technical Seismicity due to Mining Activities
Authors: V. Salajka, Z. Kaláb, J. Kala, P. Hradil
Abstract:
In the territories where high-intensity earthquakes are frequent is paid attention to the solving of the seismic problems. In the paper are described two computational model variants based on finite element method of the construction with different subsoil simulation (rigid or elastic subsoil) is used. For simulation and calculations program system based on method final elements ANSYS was used. Seismic responses calculations of residential building structure were effected on loading characterized by accelerogram for comparing with the responses spectra method.Keywords: Accelerogram, ANSYS, mining induced seismic, residential building structure, spectra, subsoil.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1538515 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease
Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly
Abstract:
Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.
Keywords: Parkinson's disease, Step method, delay differential equation, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 745514 Characterization of the In0.53Ga0.47As n+nn+ Photodetectors
Authors: Fatima Zohra Mahi, Luca Varani
Abstract:
We present an analytical model for the calculation of the sensitivity, the spectral current noise and the detective parameter for an optically illuminated In0.53Ga0.47As n+nn+ diode. The photocurrent due to the excess carrier is obtained by solving the continuity equation. Moreover, the current noise level is evaluated at room temperature and under a constant voltage applied between the diode terminals. The analytical calculation of the current noise in the n+nn+ structure is developed by considering the free carries fluctuations. The responsivity and the detection parameter are discussed as functions of the doping concentrations and the emitter layer thickness in one-dimensional homogeneous n+nn+ structure.
Keywords: Responsivity, detection parameter, photo-detectors, continuity equation, current noise.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2062513 Solving Machine Loading Problem in Flexible Manufacturing Systems Using Particle Swarm Optimization
Authors: S. G. Ponnambalam, Low Seng Kiat
Abstract:
In this paper, a particle swarm optimization (PSO) algorithm is proposed to solve machine loading problem in flexible manufacturing system (FMS), with bicriterion objectives of minimizing system unbalance and maximizing system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools. The performance of the PSO is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The results support that the proposed PSO is comparable with the algorithms reported in the literature.Keywords: Machine loading problem, FMS, Particle Swarm Optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2123512 Generalized Chebyshev Collocation Method
Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim
Abstract:
In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.
Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2641511 Non-reflection Boundary Conditions for Numerical Simulation of Supersonic Flow
Authors: A. Abdalla, A. Kaltayev
Abstract:
This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (Navier- Stocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subsonic non-reflection outflow situations. Verification of the constructed algorithm of boundary conditions is carried out by solving a test problem of perpendicular sound of jets injection into a supersonic gas flow in a plane channel.
Keywords: WENO scheme, non-reflection boundary conditions, NSCBC, supersonic flow.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2197510 Granulation using Clustering and Rough Set Theory and its Tree Representation
Authors: Girish Kumar Singh, Sonajharia Minz
Abstract:
Granular computing deals with representation of information in the form of some aggregates and related methods for transformation and analysis for problem solving. A granulation scheme based on clustering and Rough Set Theory is presented with focus on structured conceptualization of information has been presented in this paper. Experiments for the proposed method on four labeled data exhibit good result with reference to classification problem. The proposed granulation technique is semi-supervised imbibing global as well as local information granulation. To represent the results of the attribute oriented granulation a tree structure is proposed in this paper.Keywords: Granular computing, clustering, Rough sets, datamining.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1721509 The Development of Flying Type Moving Robot Using Image Processing
Authors: Suriyon Tansuriyavong, Yuuta Suzuki, Boonmee Choompol
Abstract:
Wheel-running type moving robot has the restriction on the moving range caused by obstacles or stairs. Solving this weakness, we studied the development of moving robot using airship. Our airship robot moves by recognizing arrow marks on the path. To have the airship robot recognize arrow marks, we used edge-based template matching. To control propeller units, we used PID and PD controller. The results of experiments demonstrated that the airship robot can move along the marks and can go up and down the stairs. It is shown the possibility that airship robot can become a robot which can move at wide range facilities.Keywords: Template matching, moving robot, airship robot, PID control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1538508 Environmental Inspection using WSANs Based on Multi-agent Coordination Method
Authors: Mohammad J. Heydari, Farnaz Derakhshan
Abstract:
In this paper, we focus on the problem of driving and herding a collection of autonomous actors to a given area. Then, a new method based on multi-agent coordination is proposed for solving the problem. In our proposed method, we assume that the environment is covered by sensors. When an event is occurred, sensors forward information to a sink node. Based on received information, the sink node will estimate the direction and the speed of movement of actors and announce the obtained value to the actors. The actors coordinate to reach the target location.Keywords: Coordination, Environmental Inspection, Multiagent systems, Wireless Sensor and Actor Networks (WSANs)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1434507 Solving the Quadratic Assignment Problems by a Genetic Algorithm with a New Replacement Strategy
Authors: Yongzhong Wu, Ping Ji
Abstract:
This paper proposes a genetic algorithm based on a new replacement strategy to solve the quadratic assignment problems, which are NP-hard. The new replacement strategy aims to improve the performance of the genetic algorithm through well balancing the convergence of the searching process and the diversity of the population. In order to test the performance of the algorithm, the instances in QAPLIB, a quadratic assignment problem library, are tried and the results are compared with those reported in the literature. The performance of the genetic algorithm is promising. The significance is that this genetic algorithm is generic. It does not rely on problem-specific genetic operators, and may be easily applied to various types of combinatorial problems.Keywords: Quadratic assignment problem, Genetic algorithm, Replacement strategy, QAPLIB.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2750506 Solving the Flexible Job Shop Scheduling Problem with Uniform Processing Time Uncertainty
Authors: Nasr Al-Hinai, Tarek Y. ElMekkawy
Abstract:
The performance of schedules released to a shop floor may greatly be affected by unexpected disruptions. Thus, this paper considers the flexible job shop scheduling problem when processing times of some operations are represented by a uniform distribution with given lower and upper bounds. The objective is to find a predictive schedule that can deal with this uncertainty. The paper compares two genetic approaches to obtain predictive schedule. To determine the performance of the predictive schedules obtained by both approaches, an experimental study is conducted on a number of benchmark problems.
Keywords: Genetic algorithm, met-heuristic, robust scheduling, uncertainty of processing times
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2875505 Real-Time Physics Simulation Packages: An Evaluation Study
Abstract:
This paper includes a review of three physics simulation packages that can be used to provide researchers with a virtual ground for modeling, implementing and simulating complex models, as well as testing their control methods with less cost and time of development. The inverted pendulum model was used as a test bed for comparing ODE, DANCE and Webots, while Linear State Feedback was used to control its behavior. The packages were compared with respect to model creation, solving systems of differential equation, data storage, setting system variables, control the experiment and ease of use. The purpose of this paper is to give an overview about our experience with these environments and to demonstrate some of the benefits and drawbacks involved in practice for each package.
Keywords: DANCE, Inverted Pendulum, ODE, Simulation Packages, Webots.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1570504 Analytical Study and Modeling of Free Vibrations of Functionally Graded Plates Using a Higher Shear Deformation Theory
Authors: A. Meftah, D. Zarga, M. Yahiaoui
Abstract:
In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.Keywords: FGM plates, Navier method, vibratory behavior.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 659503 A New Heuristic Algorithm for the Classical Symmetric Traveling Salesman Problem
Authors: S. B. Liu, K. M. Ng, H. L. Ong
Abstract:
This paper presents a new heuristic algorithm for the classical symmetric traveling salesman problem (TSP). The idea of the algorithm is to cut a TSP tour into overlapped blocks and then each block is improved separately. It is conjectured that the chance of improving a good solution by moving a node to a position far away from its original one is small. By doing intensive search in each block, it is possible to further improve a TSP tour that cannot be improved by other local search methods. To test the performance of the proposed algorithm, computational experiments are carried out based on benchmark problem instances. The computational results show that algorithm proposed in this paper is efficient for solving the TSPs.Keywords: Local search, overlapped neighborhood, travelingsalesman problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2225502 Analytical Solutions of Three Dimensional Steady-State Heat Transfer in Rectangular Ribs
Authors: Tao Nie, Weiqiang Liu
Abstract:
In order to obtain an accurate result of the heat transfer of the rib in the internal cooling Rectangular channel, using separation of variables, analytical solutions of three dimensional steady-state heat conduction in rectangular ribs are given by solving three dimensional steady-state function of the rectangular ribs. Therefore, we can get solution of three dimensional temperature field in the rib. Based on the solution, we can get how the Bi number affected on heat transfer. Furthermore, comparisons of the analytical and numerical results indicate agreement on temperature field in the rib.Keywords: variable separation method, analytical solution, rib, heat transfer
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2792501 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
Abstract:
In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2040500 Solving 94-bit ECDLP with 70 Computers in Parallel
Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai
Abstract:
Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1872499 New Exact Three-Wave Solutions for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System
Authors: Fadi Awawdeh, O. Alsayyed
Abstract:
New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.
Keywords: Soliton Solution, Hirota Bilinear Method, ANNV System.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1514498 Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder
Authors: T. V. S. Sekhar, B. Hema Sundar Raju
Abstract:
Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1663497 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations
Authors: A. M. Sagir
Abstract:
This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.
Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1776496 Embedded Singly Diagonally Implicit Runge-Kutta –Nystrom Method Order 5(4) for the Integration of Special Second Order ODEs
Authors: Fudziah Ismail
Abstract:
In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally implicit Runge-Kutta method. The results suggests the superiority of the new method.Keywords: Runge-Kutta Nystrom, Special second orderproblems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1667