Search results for: design equation

Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Soniya Chaudhary, Sanjeev Sahu

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Propagation of Rayleigh-type waves in a rotating piezoelectric plate is investigated. The materials are assumed to be transversely isotropic crystals. The frequency equation have been derived for electrically open and short cases. Effect of rotation and piezoelectricity have been shown. It is also found that piezoelectric material properties have an important effect on Rayleigh wave propagation. The result is relevant to the analysis and design of various acoustic surface wave devices constructed from piezoelectric materials also in SAW devices.

Keywords: rotation, frequency equation, piezoelectricity, rayleigh-type wave

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Aria Ratmandanu

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Boson stars can be viewed as zero temperature ground state, Bose-Einstein condensates, characterized by enormous occupation numbers. Time-dependent spherically symmetric spacetime can be a model of Boson Star. We use (3+1) split of Einstein equation (ADM formulation of general relativity) to solve Einstein field equation coupled to a complex scalar field (Einstein-Klein-Gordon Equation) on time-dependent spherically symmetric spacetime, We get the result that Boson stars are pulsating stars with the frequency of oscillation equal to its density. We search for interior solution of Boson stars and get the T.O.V. (Tollman-Oppenheimer-Volkoff) equation for Boson stars. Using T.O.V. equation, we get the equation of state and the relation between pressure and density, its total mass and along with its gravitational Mass. We found that the hypothetical particle Axion could form a Boson star with the size of a milky way galaxy and make it a candidate for a dark galaxy, (a galaxy that consists almost entirely of dark matter).

Keywords: axion, boson star, dark galaxy, time-dependent spherically symmetric spacetime

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Zhi Zhang, Liling Cao, Seyedbabak Momenzadeh, Lisa Davey

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Reinforced concrete (RC) flat slab-column systems are commonly used in residential or office buildings, as the flat slab provides efficient clearance resulting in more stories at a given height than regular reinforced concrete beam-slab system. Punching shear of slab-column joints is a critical component of two-way reinforced concrete flat slab design. The unbalanced moment at the joint is transferred via slab moment and shear forces. ACI 318 provides an equation to evaluate the punching shear under the design load. It is important to note that the design code considers gravity and environmental load when considering the design load combinations, while it does not consider the effect from differential foundation settlement, which may be a governing load condition for the slab design. This paper describes how prestressed reinforced concrete slab punching shear is evaluated based on ACI 318 provisions and finite element analysis. A prestressed reinforced concrete slab under differential settlements is studied using the finite element modeling methodology. The punching shear check equation is explained. The methodology to extract data for punching shear check from the finite element model is described and correlated with the corresponding code provisions. The study indicates that the finite element analysis results should be carefully reviewed and processed in order to perform accurate punching shear evaluation. Conclusions are made based on the case studies to help engineers understand the punching shear behavior in prestressed and non-prestressed reinforced concrete slabs.

Keywords: differential settlement, finite element model, prestressed reinforced concrete slab, punching shear

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Authors: Ishit Sheth, Chandrasekhar Jinendran, Chinmaya Ranjan Sahu

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A fourteen degree of freedom (DOF) ride and handling control mathematical model is developed for a car using generalized boltzmann hamel equation which will create a basis for design of ride and handling controller. Mathematical model developed yield equations of motion for non-holonomic constrained systems in quasi-coordinates. The governing differential equation developed integrates ride and handling control of car. Model-based systems engineering approach is implemented for simulation using matlab/simulink, vehicle’s response in different DOF is examined and later validated using commercial software (ADAMS). This manuscript involves detailed derivation of full car vehicle model which provides response in longitudinal, lateral and yaw motion to demonstrate the advantages of the developed model over the existing dynamic model. The dynamic behaviour of the developed ride and handling model is simulated for different road conditions.

Keywords: Full Vehicle Model, MBSE, Non Holonomic Constraints, Boltzmann Hamel Equation

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Abdelhakam A. Noreldien, Sakhr B. Abudarag, Muslim S. Eltoum, Salih O. Osman

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This paper presents an analytical study of Small Unmanned Aerial Vehicle (SUAV) dynamic stability derivatives. Simulating SUAV dynamics and analyzing its behavior at the earliest design stages is too important and more efficient design aspect. The approach suggested in this paper is using the wind tunnel experiment to collect the aerodynamic data and get the dynamic stability derivatives. AutoCAD Software was used to draw the case study (wildlife surveillance SUAV). The SUAV is scaled down to be 0.25% of the real SUAV dimensions and converted to a wind tunnel model. The model was tested in three different speeds for three different attitudes which are; pitch, roll and yaw. The wind tunnel results were then used to determine the case study stability derivative values, and hence it used to calculate the roots of the characteristic equation for both longitudinal and lateral motions. Finally, the characteristic equation roots were found and discussed in all possible cases.

Keywords: model, simulating, SUAV, wind tunnel

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Authors: Ka C. Lam, Oluwafunmibi S. Idowu

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Building girth is important in building economics and mostly used in quantities take-off of various cost items. Literature suggests that the use of conceptual quantities can improve the accuracy of cost models. Girth or perimeter of a building can be used to estimate conceptual quantities. Hence, the current paper aims to model the perimeter-area function of buildings shapes for use at the conceptual design stage. A detailed literature review on existing building shape indexes was carried out. An empirical approach was used to study the relationship between area and the shortest length of a four-sided orthogonal polygon. Finally, a mathematical approach was used to establish the observed relationships. The empirical results obtained were in agreement with the mathematical model developed. A new equation termed “conceptual perimeter equation” is proposed. The equation can be used to estimate building envelope quantities such as external wall area, external finishing area and scaffolding area before sketch or detailed drawings are prepared.

Keywords: building envelope, building shape index, conceptual quantities, cost modelling, girth

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Authors: S. Mousavian, A. Abedianpour, A. Khanmohammadi, S. Hematian, Gh. Eidi Veisi

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Distillation is one of the most important and utilized separation methods in the industrial practice. There are different ways to design of distillation column. One of these ways is short cut method. In short cut method, material balance and equilibrium are employed to calculate number of tray in distillation column. There are different methods that are classified in short cut method. One of these methods is Fenske-Underwood-Gilliland method. In this method, minimum reflux ratio should be calculated by underwood equation. Underwood proposed an equation that is useful for simple distillation column with one feed and one top and bottom product. In this study, underwood method is developed to predict minimum reflux ratio for column with one side stream upper than feed. The result of this model compared with McCabe-Thiele method. The result shows that proposed method able to calculate minimum reflux ratio with very small error.

Keywords: minimum reflux ratio, side stream, distillation, Underwood’s method

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Chang Su Woo, Hyun Sung Park

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Useful lifetime evaluations of rail-pads were very important in design procedure to assure the safety and reliability. It is, therefore, necessary to establish a suitable criterion for the replacement period of rail pads. In this study, we performed properties and accelerated heat aging tests of rail pads considering degradation factors and all environmental conditions including operation, and then derived a lifetime prediction equation according to changes in hardness, thickness, and static spring constants in the Arrhenius plot to establish how to estimate the aging of rail pads. With the useful lifetime prediction equation, the lifetime of e-clip pads was 2.5 years when the change in hardness was 10% at 25°C; and that of f-clip pads was 1.7 years. When the change in thickness was 10%, the lifetime of e-clip pads and f-clip pads is 2.6 years respectively. The results obtained in this study to estimate the useful lifetime of rail pads for high speed trains can be used for determining the maintenance and replacement schedule for rail pads.

Keywords: rail pads, accelerated test, Arrhenius plot, useful lifetime prediction, mechanical engineering design

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: Manisha Kankarej

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The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

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Authors: Matheus Fernando Pereira, Varese Salvador Timoteo

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In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.

Keywords: advection-diffusion equation, dispersion, numerical methods, pulse-type source

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Authors: Ted Silva

Abstract:

Dietrich de Velsa's Équation à un inconnu / Equation to an Unknown hybridizes art cinema style with the sexually explicit aesthetics of pornography to envision a uniquely queer world unmoored by heteronormative influence. This stylization evokes the memory of a queer history that once approximated such a prospect. With this historical and political context in mind, this paper utilizes formal analysis to assess how the film frames queer sexual encounters as tender acts of care, sometimes literally mending physical wounds. However, Equation to Unknown also highlights the transience of these sexual exchanges. By emphasizing the homogeneity of the protagonist’s sexual conquests, the film reveals that these practices have a darker meaning when the men reject the individualized connection to pursue purely visceral gratification. Given the lack of diversity or even recognizable identifying factors, the men become more anonymous to each other the more they pair up. Ultimately, Equation to an Unknown both celebrates and problematizes its vision of a queer utopia, highlighting areas in the community wherein intimacy and care flourish and locating those spots in which they are neglected.

Keywords: pornography studies, queer cinema, French cinema, history

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Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: optimal control, stochastic systems, quantum systems, stabilization

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Authors: T. Yilmaz, N. Kirac

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Beam-column elements are defined as structural members subjected to a combination of axial and bending forces. Lateral torsional buckling is one of the major failure modes in which beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting. This study presents a compact closed-form equation that it can be used for calculating critical lateral torsional-buckling load of beam-columns with monosymmetric sections in the presence of a known axial load. Lateral-torsional buckling behavior of beam-columns subjected to constant axial force and various transverse load cases are investigated by using Ritz method in order to establish proposed equation. Lateral-torsional buckling loads calculated by presented formula are compared to finite element model results. ABAQUS software is utilized to generate finite element models of beam-columns. It is found out that lateral-torsional buckling load of beam-columns with monosymmetric sections can be determined by proposed equation and can be safely used in design.

Keywords: lateral-torsional buckling, stability, beam-column, monosymmetric section

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Authors: Toufic Abd El-Latif Sadek

Abstract:

The Asphalt object represents the asphalted areas, like roads. The best original data of thermal images occurred at a specific time during the days of the year, by preventing the gaps in times which give the close and same brightness from different objects, using seven sample objects, asphalt, concrete, metal, rock, dry soil, vegetation, and water. It has been found in this study a general timing equation for capturing satellite thermal images at different locations, depends on a fixed time the sunrise and sunset; Capture Time= Tcap =(TM*TSR) ±TS.

Keywords: asphalt, satellite, thermal images, timing equation

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Maryam Hasanali, Syed Mohammad Mojtabaei, Iman Hajirasouliha, G. Charles Clifton, James B. P. Lim

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Cold-formed steel (CFS) elements are increasingly being used as main load-bearing components in the modern construction industry, including low- to mid-rise buildings. In typical multi-storey buildings, CFS structural members act as beam-column elements since they are exposed to combined axial compression and bending actions, both in moment-resisting frames and stud wall systems. Current design specifications, including the American Iron and Steel Institute (AISI S100) and the Australian/New Zealand Standard (AS/NZS 4600), neglect the beneficial effects of warping-restrained boundary conditions in the design of beam-column elements. Furthermore, while a non-linear relationship governs the interaction of axial compression and bending, the combined effect of these actions is taken into account through a simplified linear expression combining pure axial and flexural strengths. This paper aims to evaluate the reliability of the well-known Direct Strength Method (DSM) as well as design proposals found in the literature to provide a better understanding of the efficiency of the code-prescribed linear interaction equation in the strength predictions of CFS beam columns and the effects of warping-restrained boundary conditions on their behavior. To this end, the experimentally validated finite element (FE) models of CFS elements under compression and bending were developed in ABAQUS software, which accounts for both non-linear material properties and geometric imperfections. The validated models were then used for a comprehensive parametric study containing 270 FE models, covering a wide range of key design parameters, such as length (i.e., 0.5, 1.5, and 3 m), thickness (i.e., 1, 2, and 4 mm) and cross-sectional dimensions under ten different load eccentricity levels. The results of this parametric study demonstrated that using the DSM led to the most conservative strength predictions for beam-column members by up to 55%, depending on the element’s length and thickness. This can be sourced by the errors associated with (i) the absence of warping-restrained boundary condition effects, (ii) equations for the calculations of buckling loads, and (iii) the linear interaction equation. While the influence of warping restraint is generally less than 6%, the code suggested interaction equation led to an average error of 4% to 22%, based on the element lengths. This paper highlights the need to provide more reliable design solutions for CFS beam-column elements for practical design purposes.

Keywords: beam-columns, cold-formed steel, finite element model, interaction equation, warping-restrained boundary conditions

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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