Search results for: Meshless spectrally convergent
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 66

Search results for: Meshless spectrally convergent

66 Extended Arithmetic Precision in Meshfree Calculations

Authors: Edward J. Kansa, Pavel Holoborodko

Abstract:

Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: Meshless spectrally convergent, partial differential equations, extended arithmetic precision, no branching.

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65 Several Spectrally Non-Arbitrary Ray Patterns of Order 4

Authors: Ling Zhang, Feng Liu

Abstract:

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

Keywords: Spectrally arbitrary, Nilpotent matrix, Ray patterns, sign patterns.

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64 Implementation of Meshless FEM for Engineering Applications

Authors: A. Seidl, Th. Schmidt

Abstract:

Meshless Finite Element Methods, namely element-free Galerkin and point-interpolation method were implemented and tested concerning their applicability to typical engineering problems like electrical fields and structural mechanics. A class-structure was developed which allows a consistent implementation of these methods together with classical FEM in a common framework. Strengths and weaknesses of the methods under investigation are discussed. As a result of this work joint usage of meshless methods together with classical Finite Elements are recommended.

Keywords: Finite Elements, meshless, element-free Galerkin, point-interpolation.

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63 Applying Element Free Galerkin Method on Beam and Plate

Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, element-free Galerkin, moving least squares, meshless methods.

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62 Parametric Analysis and Optimal Design of Functionally Graded Plates Using Particle Swarm Optimization Algorithm and a Hybrid Meshless Method

Authors: Foad Nazari, Seyed Mahmood Hosseini, Mohammad Hossein Abolbashari, Mohammad Hassan Abolbashari

Abstract:

The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.

Keywords: Optimal design, natural frequency, FG plate, hybrid meshless method, MLPG method, ANN approach, particle swarm optimization.

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61 CFD Effect of the Tidal Grating in Opposite Directions

Authors: N. M. Thao, I. Dolguntseva, M. Leijon

Abstract:

Flow blockages referring to the increase in flow are being considered as a vital equipment for marine current energy conversion. However, the shape of these devices will result in extracted energy under the operation. The present work investigates the effect of two configurations of a grating, convergent and divergent that located upstream, to the water flow velocity. The flow characteristics are studied by Computational Fluid Dynamic simulation by using the ANSYS Fluent solver for these specified arrangements of the grating. The results indicate that distinguished characteristics of flow velocity between “convergent” and “divergent” grating placements is up to 10% in confined conditions. Furthermore, the velocity in case of convergent grating is higher than that of divergent grating.

Keywords: Marine current energy, marine current energy converter, turbine grating, RANS simulation, water flow velocity.

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60 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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59 Effect of Initial Conditions on Aerodynamic and Acoustic Characteristics of High Subsonic Jets from Sharp Edged Circular Orifice

Authors: Murugan, K. N. Sharma, S. D.

Abstract:

The present work involves measurements to examine the effects of initial conditions on aerodynamic and acoustic characteristics of a Jet at M=0.8 by changing the orientation of sharp edged orifice plate. A thick plate with chamfered orifice presented divergent and convergent openings when it was flipped over. The centerline velocity was found to decay more rapidly for divergent orifice and that was consistent with the enhanced mass entrainment suggesting quicker spread of the jet compared with that from the convergent orifice. The mixing layer region elucidated this effect of initial conditions at an early stage – the growth was found to be comparatively more pronounced for the divergent orifice resulting in reduced potential core size. The acoustic measurements, carried out in the near field noise region outside the jet within potential core length, showed the jet from the divergent orifice to be less noisy. The frequency spectra of the noise signal exhibited that in the initial region of comparatively thin mixing layer for the convergent orifice, the peak registered a higher SPL and a higher frequency as well. The noise spectra and the mixing layer development suggested a direct correlation between the coherent structures developing in the initial region of the jet and the noise captured in the surrounding near field.

Keywords: Convergent orifice jet, Divergent orifice jet, Mass entrainment, mixing layer, near field noise, frequency spectrum, SPL, Strouhal number, wave number, reactive pressure field, propagating pressure field.

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58 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

Authors: Menglong Su, Shaoyun Shi, Qing Xu

Abstract:

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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57 Development and Validation of Employee Trust Scale: Factor Structure, Reliability and Validity

Authors: Chua Bee Seok, Getrude Cosmas, Jasmine Adela Mutang, Shazia Iqbal Hashmi

Abstract:

The aim of this study was to determine the factor structure and psychometric properties (i.e., reliability and convergent validity) of the Employee Trust Scale, a newly created instrument by the researchers. The Employee Trust Scale initially contained 82 items to measure employees’ trust toward their supervisors. A sample of 818 (343 females, 449 males) employees were selected randomly from public and private organization sectors in Kota Kinabalu, Sabah, Malaysia. Their ages ranged from 19 to 67 years old with a mean of 34.55 years old. Their average tenure with their current employer was 11.2 years (s.d. = 7.5 years). The respondents were asked to complete the Employee Trust Scale, as well as a managerial trust questionnaire from Mishra. The exploratory factor analysis on employees’ trust toward their supervisor’s extracted three factors, labeled ‘trustworthiness’ (32 items), ‘position status’ (11 items) and ‘relationship’ (6 items) which accounted for 62.49% of the total variance. Trustworthiness factors were re-categorized into three sub factors: competency (11 items), benevolence (8 items) and integrity (13 items). All factors and sub factors of the scales demonstrated clear reliability with internal consistency of Cronbach’s Alpha above .85. The convergent validity of the Scale was supported by an expected pattern of correlations (positive and significant correlation) between the score of all factors and sub factors of the scale and the score on the managerial trust questionnaire, which measured the same construct. The convergent validity of Employee Trust Scale was further supported by the significant and positive inter-correlation between the factors and sub factors of the scale. The results suggest that the Employee Trust Scale is a reliable and valid measure. However, further studies need to be carried out in other groups of sample as to further validate the Scale.

Keywords: Employees trust scale, position status, psychometric properties, relationship, trustworthiness.

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56 Application of De-Laval Nozzle Transonic Flow Field Computation Approaches

Authors: A. Haddad, H. Kbab

Abstract:

A supersonic expansion cannot be achieved within a convergent-divergent nozzle if the flow velocity does not reach that of the sound at the throat. The computation of the flow field characteristics at the throat is thus essential to the nozzle developed thrust value and therefore to the aircraft or rocket it propels. Several approaches were developed in order to describe the transonic expansion, which takes place through the throat of a De-Laval convergent-divergent nozzle. They all allow reaching good results but showing a major shortcoming represented by their inability to describe the transonic flow field for nozzles having a small throat radius. The approach initially developed by Kliegel & Levine uses the velocity series development in terms of the normalized throat radius added to unity instead of solely the normalized throat radius or the traditional small disturbances theory approach. The present investigation carries out the application of these three approaches for different throat radiuses of curvature. The method using the normalized throat radius added to unity shows better results when applied to geometries integrating small throat radiuses.

Keywords: De-Laval nozzles, transonic calculations, transonic flow, supersonic nozzle.

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55 Malaysian Multi-Ethnic Discrimination Scale: Preliminary Factor and Psychometric Analysis

Authors: Chua Bee Seok, Shamsul Amri Baharuddin, Rosnah Ismail, Ferlis Bahari, Jasmine Adela Mutang, Lailawati Madlan, Asong Joseph

Abstract:

The aims of this study were to determine the factor structure and psychometric properties (i.e., reliability and convergent validity) of the Malaysian Multi-Ethnic Discrimination Scale (MMEDS). It consists of 71-items measure experience, strategies used and consequences of ethnic discrimination. A sample of 649 university students from one of the higher education institution in Malaysia was asked to complete MMEDS, as well as Perceived Ethnic and Racial Discrimination. The exploratory factor analysis on ethnic discrimination experience extracted two factors labeled ‘unfair treatment’ (15 items) and ‘Denial of the ethnic right’ (12 items) which accounted for 60.92% of the total variance. The two sub scales demonstrated clear reliability with internal consistency above .70. The convergent validity of the Scale was supported by an expected pattern of correlations (positive and significant correlation) between the score of unfair treatment and denial of the ethnic right and the score of Perceived Ethnic and Racial Discrimination by Peers Scale. The results suggest that the MMEDS is a reliable and valid measure. However, further studies need to be carried out in other groups of sample as to validate the Scale.

Keywords: Factor structure, psychometric properties, exploratory factor analysis.

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54 RBF- based Meshless Method for Free Vibration Analysis of Laminated Composite Plates

Authors: Jeeoot Singh, Sandeep Singh, K. K. Shukla

Abstract:

The governing differential equations of laminated plate utilizing trigonometric shear deformation theory are derived using energy approach. The governing differential equations discretized by different radial basis functions are used to predict the free vibration behavior of symmetric laminated composite plates. Effect of orthotropy and span to thickness ratio on frequency parameter of simply supported laminated plate is presented. Numerical results show the accuracy and good convergence of radial basis functions.

Keywords: Composite plates, Meshfree method, free vibration, Shear deformation, RBFs

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53 Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach

Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

Abstract:

Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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52 A Meshfree Solution of Tow-Dimensional Potential Flow Problems

Authors: I. V. Singh, A. Singh

Abstract:

In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.

Keywords: Meshless, EFG method, potential flow, Lagrange multiplier method, penalty method, penalty parameter and scaling parameter

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51 On λ− Summable of Orlicz Space of Gai Sequences of Fuzzy Numbers

Authors: N.Subramanian, S.Krishnamoorthy, S. Balasubramanian

Abstract:

In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.

Keywords: Fuzzy numbers, statistical convergence, Orlicz space, gai sequence.

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50 On λ− Summable of Orlicz Space of Entire Sequences of Fuzzy Numbers

Authors: N. Subramanian, U. K. Misra, M. S. Panda

Abstract:

In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.

Keywords: Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.

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49 The Error Analysis of An Upwind Difference Approximation for a Singularly Perturbed Problem

Authors: Jiming Yang

Abstract:

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

Keywords: Singularly perturbed, upwind difference, uniform convergence.

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48 Simulation of the Reactive Rotational Molding Using Smoothed Particle Hydrodynamics

Authors: A. Hamidi, S. Khelladi, L. Illoul, A. Tcharkhtchi

Abstract:

Reactive rotational molding (RRM) is a process to manufacture hollow plastic parts with reactive material has several advantages compared to conventional roto molding of thermoplastic powders: process cycle time is shorter; raw material is less expensive because polymerization occurs during processing and high-performance polymers may be used such as thermosets, thermoplastics or blends. However, several phenomena occur during this process which makes the optimization of the process quite complex. In this study, we have used a mixture of isocyanate and polyol as a reactive system. The chemical transformation of this system to polyurethane has been studied by thermal analysis and rheology tests. Thanks to these results of the curing process and rheological measurements, the kinetic and rheokinetik of polyurethane was identified. Smoothed Particle Hydrodynamics, a Lagrangian meshless method, was chosen to simulate reactive fluid flow in 2 and 3D configurations of the polyurethane during the process taking into account the chemical, and chemiorehological results obtained experimentally in this study.

Keywords: Reactive rotational molding, free surface flows, simulation, smoothed particle hydrodynamics, surface tension.

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47 A Performance Comparison of Golay and Reed-Muller Coded OFDM Signal for Peak-to-Average Power Ratio Reduction

Authors: Sanjay Singh, M Sathish Kumar, H. S Mruthyunjaya

Abstract:

Multicarrier transmission system such as Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for high bit rate transmission in wireless communication systems. OFDM is a spectrally efficient modulation technique that can achieve high speed data transmission over multipath fading channels without the need for powerful equalization techniques. A major drawback of OFDM is the high Peak-to-Average Power Ratio (PAPR) of the transmit signal which can significantly impact the performance of the power amplifier. In this paper we have compared the PAPR reduction performance of Golay and Reed-Muller coded OFDM signal. From our simulation it has been found that the PAPR reduction performance of Golay coded OFDM is better than the Reed-Muller coded OFDM signal. Moreover, for the optimum PAPR reduction performance, code configuration for Golay and Reed-Muller codes has been identified.

Keywords: OFDM, PAPR, Perfect Codes, Golay Codes, Reed-Muller Codes

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46 On Constructing a Cubically Convergent Numerical Method for Multiple Roots

Authors: Young Hee Geum

Abstract:

We propose the numerical method defined by

xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N,

and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: Asymptotic error constant, iterative method , multiple root, root-finding.

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45 Some Results on Preconditioned Modified Accelerated Overrelaxation Method

Authors: Guangbin Wang, Deyu Sun, Fuping Tan

Abstract:

In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.

Keywords: preconditioned, MAOR method, linear system, convergence, comparison.

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44 Capacity Optimization for Local and Cooperative Spectrum Sensing in Cognitive Radio Networks

Authors: Ayman A. El-Saleh, Mahamod Ismail, Mohd. A. M. Ali, Ahmed N. H. Alnuaimy

Abstract:

The dynamic spectrum allocation solutions such as cognitive radio networks have been proposed as a key technology to exploit the frequency segments that are spectrally underutilized. Cognitive radio users work as secondary users who need to constantly and rapidly sense the presence of primary users or licensees to utilize their frequency bands if they are inactive. Short sensing cycles should be run by the secondary users to achieve higher throughput rates as well as to provide low level of interference to the primary users by immediately vacating their channels once they have been detected. In this paper, the throughput-sensing time relationship in local and cooperative spectrum sensing has been investigated under two distinct scenarios, namely, constant primary user protection (CPUP) and constant secondary user spectrum usability (CSUSU) scenarios. The simulation results show that the design of sensing slot duration is very critical and depends on the number of cooperating users under CPUP scenario whereas under CSUSU, cooperating more users has no effect if the sensing time used exceeds 5% of the total frame duration.

Keywords: Capacity, cognitive radio, optimization, spectrumsensing.

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43 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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42 Outdoor Anomaly Detection with a Spectroscopic Line Detector

Authors: O. J. G. Somsen

Abstract:

One of the tasks of optical surveillance is to detect anomalies in large amounts of image data. However, if the size of the anomaly is very small, limited information is available to distinguish it from the surrounding environment. Spectral detection provides a useful source of additional information and may help to detect anomalies with a size of a few pixels or less. Unfortunately, spectral cameras are expensive because of the difficulty of separating two spatial in addition to one spectral dimension. We investigate the possibility of modifying a simple spectral line detector for outdoor detection. This may be especially useful if the area of interest forms a line, such as the horizon. We use a monochrome CCD that also enables detection into the near infrared. A simple camera is attached to the setup to determine which part of the environment is spectrally imaged. Our preliminary results indicate that sensitive detection of very small targets is indeed possible. Spectra could be taken from the various targets by averaging columns in the line image. By imaging a set of lines of various widths we found narrow lines that could not be seen in the color image but remained visible in the spectral line image. A simultaneous analysis of the entire spectra can produce better results than visual inspection of the line spectral image. We are presently developing calibration targets for spatial and spectral focusing and alignment with the spatial camera. This will present improved results and more use in outdoor application.

Keywords: Anomaly detection, spectroscopic line imaging, image analysis.

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41 Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems

Authors: Shengfeng Li, Rujing Wang

Abstract:

In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.

Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.

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40 Some Results on New Preconditioned Generalized Mixed-Type Splitting Iterative Methods

Authors: Guangbin Wang, Fuping Tan, Deyu Sun

Abstract:

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.

Keywords: Preconditioned, GMTS method, linear system, convergence, comparison.

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39 Design of the Propelling Nozzles for the Launchers and Satellites

Authors: R. Haoui

Abstract:

The aim of this work is to determine the supersonic nozzle profiles used in propulsion, for the launchers or embarked with the satellites. This design has as a role firstly, to give a important propulsion, i.e. with uniform and parallel flow at exit, secondly to find a short length profiles without modification of the flow in the nozzle. The first elaborate program is used to determine the profile of divergent by using the characteristics method for an axisymmetric flow. The second program is conceived by using the finite volume method to determine and test the profile found connected to a convergent.

Keywords: Characteristic method, nozzles, supersonic flow, propellers.

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38 Solving the Economic Dispatch Problem by Using Differential Evolution

Authors: S. Khamsawang, S. Jiriwibhakorn

Abstract:

This paper proposes an application of the differential evolution (DE) algorithm for solving the economic dispatch problem (ED). Furthermore, the regenerating population procedure added to the conventional DE in order to improve escaping the local minimum solution. To test performance of DE algorithm, three thermal generating units with valve-point loading effects is used for testing. Moreover, investigating the DE parameters is presented. The simulation results show that the DE algorithm, which had been adjusted parameters, is better convergent time than other optimization methods.

Keywords: Differential evolution, Economic dispatch problem, Valve-point loading effect, Optimization method.

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37 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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