Search results for: Runge's phenomenon.

Authors: A. Zerarka, A. Soukeur, N. Khelil

Abstract:

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

Keywords: Integral equation, particle swarm optimization, Runge's phenomenon.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: Expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon.

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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.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

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In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.

Keywords: Electrically conducting elastico-viscous fluid, symmetry solution, Homotopy perturbation method, Padé approximation, 4th order Runge–Kutta, Maple

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Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

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Taking into account that many problems of natural sciences and engineering are reduced to solving initial-value problem for ordinary differential equations, beginning from Newton, the scientists investigate approximate solution of ordinary differential equations. There are papers of different authors devoted to the solution of initial value problem for ODE. The Euler-s known method that was developed under the guidance of the famous scientists Adams, Runge and Kutta is the most popular one among these methods. Recently the scientists began to construct the methods preserving some properties of Adams and Runge-Kutta methods and called them hybrid methods. The constructions of such methods are investigated from the middle of the XX century. Here we investigate one generalization of multistep and hybrid methods and on their base we construct specific methods of accuracy order p = 5 and p = 6 for k = 1 ( k is the order of the difference method).

Keywords: Multistep and hybrid methods, initial value problem, degree and stability of hybrid methods

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Authors: N. Zaki Alamdari, M. Banihashemi, A. Mirghasemi

Abstract:

To estimate the risks of dam failure phenomenon, it is necessary to understand this phenomenon and the involved governing factors. Overtopping and piping are the two main reasons of earthdam failures. In the piping context, the piping is determined as a phenomenon which is occurred between two phases, the water liquid and the solid soil. In this investigation, the onset of piping and its development, as well as the movement of water in soil, are numerically approached. In this regard, a one-dimensional numerical model based on the mass-conserving finite-volume method is developed and applied in order to simulate the piping phenomenon in a continuous circular tunnel of given initial length and radius, located between upstream and downstream. The simulation result includes the time-variations of radius along the tunnel until the radius value reaches its critical and the piping phenomenon converts to overtopping.

Keywords: Earth dam, dam break, piping, internal erosion

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Authors: W. Lai, A. A. Khan

Abstract:

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing Runge- Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.

Keywords: Discontinuous finite element, TVD Runge-Kuttascheme, slope limiters, Riemann solvers, shallow water flow.

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Authors: M. A. Omoloye, M. I. Yusuff, O. K. S. Emiola

Abstract:

The use of mathematical models for solving biological problems varies from simple to complex analyses, depending on the nature of the research problems and applicability of the models. The method is more common nowadays. Many complex models become impractical when transmitted analytically. However, alternative approach such as numerical method can be employed. It appropriateness in solving linear and non-linear model equation in Differential Transformation Method (DTM) which depends on Taylor series make it applicable. Hence this study investigates the application of DTM to solve dynamic transmission of Lassa fever model in a population. The mathematical model was formulated using first order differential equation. Firstly, existence and uniqueness of the solution was determined to establish that the model is mathematically well posed for the application of DTM. Numerically, simulations were conducted to compare the results obtained by DTM and that of fourth-order Runge-Kutta method. As shown, DTM is very effective in predicting the solution of epidemics of Lassa fever model.

Keywords: Differential Transform Method, Existence and uniqueness, Lassa fever, Runge-Kutta Method.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

Abstract:

The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a  mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.

Keywords: Asymptotic stability, incubation period, Routh-Hurwitz criterion, Runge Kutta method.

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Authors: H. Taheri Shahraiyni, B. Ataie Ashtiani

Abstract:

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The numerical solutions of two problems were compared using four evaluation criteria and the results of comparisons showed that fully implicit scheme is better than the other schemes. In addition, utilizing of standard chord slope method for approximation of moisture capacity function, automatic time stepping method and difference between two successive iterations as convergence criterion in the fully implicit scheme can lead to better and more reliable results for simulation of fluid movement in different unsaturated soils.

Keywords: Finite Difference methods, Richards equation, fullyimplicit, Crank-Nicolson, Runge-Kutta.

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Authors: Marita Canina, Carmen Bruno

Abstract:

Digital Do It Yourself (DIY) is a contemporary socio-technological phenomenon, enabled by technological tools. The nature and potential long-term effects of this phenomenon have been widely studied within the framework of the EU funded project ‘Digital Do It Yourself’, in which the authors have created and experimented a specific Digital Do It Yourself (DiDIY) co-design process. The phenomenon was first studied through a literature research to understand its multiple dimensions and complexity. Therefore, co-design workshops were used to investigate the phenomenon by involving people to achieve a complete understanding of the DiDIY practices and its enabling factors. These analyses allowed the definition of the DiDIY fundamental factors that were then translated into a design tool. The objective of the tool is to shape design concepts by transferring these factors into different environments to achieve innovation. The aim of this paper is to present the ‘DiDIY Factor Stimuli’ tool, describing the research path and the findings behind it.

Keywords: Co-design process, digital DIY, innovation, toolkit.

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Authors: Hyein Ko

Abstract:

In 2017, many signs of populism occurred around the world. This paper suggests that populism is not a sudden phenomenon, but a manifestation of common people’s will. By analyzing previous research, this paper proposes three factors related to populism: Inequality, experience of economic crisis, and rapid cultural change. With these three elements, four cases will be investigated in this article; two countries experienced populism, and the other two countries did not experience it. Comparing four cases by using three elements will give a fruitful foundation for further analysis regarding populism. In sum, aforementioned three elements are highly related to the occurrence of populism. However, there is one hidden factor: dissatisfaction with established politics. Thus, populism is not a temporal phenomenon. It is a red alert for democratic crisis.

Keywords: Common people, democratic crisis, populism, Trump phenomenon.

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Authors: Jihye Jeon

Abstract:

This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: Multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon.

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Authors: Asmaa Amehraye, Dominique Pastor, Ahmed Tamtaoui, Driss Aboutajdine

Abstract:

A new analysis of perceptual speech enhancement is presented. It focuses on the fact that if only noise above the masking threshold is filtered, then noise below the masking threshold, but above the absolute threshold of hearing, can become audible after the masker filtering. This particular drawback of some perceptual filters, hereafter called the maskee-to-audible-noise (MAN) phenomenon, favours the emergence of isolated tonals that increase musical noise. Two filtering techniques that avoid or correct the MAN phenomenon are proposed to effectively suppress background noise without introducing much distortion. Experimental results, including objective and subjective measurements, show that these techniques improve the enhanced speech quality and the gain they bring emphasizes the importance of the MAN phenomenon.

Keywords: Perceptual speech filtering, maskee to audible noise, distorsion, musical noise.

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Authors: V. G. Cappellesso, D. M. G. da Silva, J. A. Arndt, N. dos Santos Petry, A. B. Masuero, D. C. C. Dal Molin

Abstract:

Concrete elements are subject to cracking, which can be an access point for deleterious agents that can trigger pathological manifestations reducing the service life of these structures. Finding ways to minimize or eliminate the effects of this aggressive agents’ penetration, such as the sealing of these cracks, is a manner of contributing to the durability of these structures. The cementitious self-healing phenomenon can be classified in two different processes. The autogenous self-healing that can be defined as a natural process in which the sealing of this cracks occurs without the stimulation of external agents, meaning, without different materials being added to the mixture, while on the other hand, the autonomous seal-healing phenomenon depends on the insertion of a specific engineered material added to the cement matrix in order to promote its recovery. This work aims to evaluate the autogenous self-healing of concretes produced with different water/cement ratios and exposed to wet/dry cycles, considering two ages of crack openings, 3 days and 28 days. The self-healing phenomenon was evaluated using two techniques: crack healing measurement using ultrasonic waves and image analysis performed with an optical microscope. It is possible to observe that by both methods, it possible to observe the self-healing phenomenon of the cracks. For young ages of crack openings and lower water/cement ratios, the self-healing capacity is higher when compared to advanced ages of crack openings and higher water/cement ratios. Regardless of the crack opening age, these concretes were found to stabilize the self-healing processes after 80 days or 90 days.

Keywords: Self-healing, autogenous, water/cement ratio, curing cycles, test methods.

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Authors: Hoda Molavi, Sima Hoseinpoor, Hossein Bahmanyar

Abstract:

A Rotary Disc Contactor with inner diameter of 9.1cm and maximum operating height of 40cm has been used to investigate break up phenomenon. Water-Toluene, Water as continuous phase and Toluene as dispersed phase, was selected as chemical system in the experiments. The mentioned chemical system has high interfacial tension so it was possible to form big drops which permit accurate investigation on break up phenomenon as well as the first and second critical rotor speeds. In this study, Break up phenomenon has been studied as a function of mother drop size, rotor speed and continuous phase height. Further more; the effects of mother drop size and continuous phase height on the first and second critical rotor speeds were investigated. Finally, two modified correlations were proposed to estimate the first and second critical speeds.

Keywords: Breakage, First critical rotor speed, Rotary disccontactor, Second critical rotor speed

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Authors: Huda Ahmed Al Taisan

Abstract:

This paper investigates a phonological phenomenon, which exhibits variation ‘alternation’ in terms of the uvular consonants [q] and [ʁ] in Hasawi Arabic. This dialect is spoken in Alahsa city, which is located in the Eastern province of Saudi Arabia. To the best of our knowledge, no such research has systematically studied this phenomenon in Hasawi Arabic dialect. This paper is significant because it fills the gap in the literature about this alternation phenomenon in this understudied dialect. A large amount of the data is extracted from several interviews the author has conducted with 10 participants, native speakers of the dialect, and complemented by additional forms from social media. The latter method of collecting the data adds to the significance of the research. The analysis of the data is carried out in Harmonic Serialism Optimality Theory (HS-OT), a version of the Optimality Theoretic (OT) framework, which holds that linguistic forms are the outcome of the interaction among violable universal constraints, and in the recent development of OT into a model that accounts for linguistic variation in harmonic derivational steps. This alternation process is assumed to be phonologically unconditioned and in free variation in other varieties of Arabic dialects in the area. The goal of this paper is to investigate whether this phenomenon is in free variation or governed, what governs this alternation between [q] and [ʁ] and whether the alternation is phonological or other linguistic constraints are in action. The results show that the [q] and [ʁ] alternation is not free and it occurs due to different assimilation processes. Positional, segmental sequence and vowel adjacency factors are in action in Hasawi Arabic.

Keywords: Harmonic serialism, Hasawi, uvular, alternation.

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Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani

Abstract:

A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.

Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam

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Authors: Mahmoud Zarrini, R.N. Pralhad

Abstract:

In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.

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Authors: Gholamreza Zahedi, M. Tarin, M. Biglari

Abstract:

This work investigated the steady state and dynamic simulation of a fixed bed industrial naphtha reforming reactors. The performance of the reactor was investigated using a heterogeneous model. For process simulation, the differential equations are solved using the 4th order Runge-Kutta method .The models were validated against measured process data of an existing naphtha reforming plant. The results of simulation in terms of components yields and temperature of the outlet were in good agreement with empirical data. The simple model displays a useful tool for dynamic simulation, optimization and control of naphtha reforming.

Keywords: Dynamic simulation, fixed bed reactor, modeling, reforming

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Authors: Sh. Hamada, N. Burtebayev, N. Amangeldi, A. Amar

Abstract:

The aim of this work is to study the elastic transfer phenomenon which takes place in the elastic scattering of 16O on 12C at energies near the Coulomb barrier. Where, the angular distribution decrease steadily with increasing the scattering angle, then the cross section will increase at backward angles due to the α-transfer process. This reaction was also studied at different energies for tracking the nuclear rainbow phenomenon. The experimental data of the angular distribution at these energies were compared to the calculation predictions. The optical potential codes such as SPIVAL and Distorted Wave Born Approximation (DWUCK5) were used in analysis.

Keywords: Transfer reaction, DWBA, Elastic Scattering, Optical Potential Codes.

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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.

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