Search results for: first order shear deformationtheory.

Authors: A. Nedjar, S. Aguib, M. Meloussi, T. Djedid, A. Khebli, R. Harhout, L. Kobzili, N. Chikh, M. Tourab

Abstract:

Finding the mechanical properties of magnetorheological elastomers (MREs) is fundamental to create smart materials and devices with desired properties and functionalities. The MREs properties, in shear mode, have been extensively investigated, but these have been less exploited with frequency-temperature dependence. In this article, we studied the performance of MREs with frequency-temperature dependence. The elastic modulus, loss modulus and loss factor of MREs were studied under different temperature values; different values of the magnetic field and different values of the frequency. The results found showed the interest of these active materials in different industrial sectors.

Keywords: Magnetorheological elastomer, mechanical behavior, frequency, temperature.

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

Abstract:

A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: Sharifullah Ahmed, Sarwar Jahan Md. Yasin

Abstract:

Shallow foundations on unimproved soft natural soils can undergo a high consolidation and secondary settlement. For low and medium rise building projects on such soil condition, pile foundation may not be cost effective. In such cases an alternative to pile foundations may be shallow strip footings placed on a double layered improved soil system soil. The upper layer of this system is untreated or cement treated compacted sand and underlying layer is natural soft clay. This system will reduce the settlement to an allowable limit. The current research has been conducted with the settlement of a rigid plane-strain strip footing of 2.5 m width placed on the surface of a soil consisting of an untreated or cement treated sand layer overlying a bed of homogeneous soft clay. The settlement of the mentioned shallow foundation has been studied considering both cases with the thicknesses of the sand layer are 0.3 to 0.9 times the width of footing. The response of the clay layer is assumed as undrained for plastic loading stages and drained during consolidation stages. The response of the sand layer is drained during all loading stages. FEM analysis was done using PLAXIS 2D Version 8.0. A natural clay deposit of 15 m thickness and 18 m width has been modeled using Hardening Soil Model, Soft Soil Model, Soft Soil Creep Model, and upper improvement layer has been modeled using only Hardening Soil Model. The groundwater level is at the top level of the clay deposit that made the system fully saturated. Parametric study has been conducted to determine the effect of thickness, density, cementation of the sand mat and density, shear strength of the soft clay layer on the settlement of strip foundation under the uniformly distributed vertical load of varying value. A set of the chart has been established for designing shallow strip footing on the sand mat over thick, soft clay deposit through obtaining the particular thickness of sand mat for particular subsoil parameter to ensure no punching shear failure and no settlement beyond allowable level. Design guideline in the form of non-dimensional charts has been developed for footing pressure equivalent to medium-rise residential or commercial building foundation with strip footing on soft inorganic Normally Consolidated (NC) soil of Bangladesh having void ratio from 1.0 to 1.45.

Keywords: Design charts, ground improvement, PLAXIS 2D, primary and secondary settlement, sand Mat, soft clay.

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Authors: T. K. V. Iyengar, Punnamchandar Bitla

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The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.

Keywords: Pulsating flow, couple stress fluid, permeable beds, mass flux, shear stress.

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Authors: Birs Isabela, Muresan Cristina, Folea Silviu, Prodan Ovidiu

Abstract:

The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.

Keywords: Fractional order controller, piezoelectric actuators, smart beam, vibration suppression.

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Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang

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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.

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Authors: Rameswar Debnath, Haruhisa Takahashi

Abstract:

An evolutionary method whose selection and recombination operations are based on generalization error-bounds of support vector machine (SVM) can select a subset of potentially informative genes for SVM classifier very efficiently [7]. In this paper, we will use the derivative of error-bound (first-order criteria) to select and recombine gene features in the evolutionary process, and compare the performance of the derivative of error-bound with the error-bound itself (zero-order) in the evolutionary process. We also investigate several error-bounds and their derivatives to compare the performance, and find the best criteria for gene selection and classification. We use 7 cancer-related human gene expression datasets to evaluate the performance of the zero-order and first-order criteria of error-bounds. Though both criteria have the same strategy in theoretically, experimental results demonstrate the best criterion for microarray gene expression data.

Keywords: support vector machine, generalization error-bound, feature selection, evolutionary algorithm, microarray data

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil

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In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

Keywords: Reduced Order Modeling, Stability, Mihailov Stability Criterion, Continued Fraction Expansions, Differential Evolution, Integral Squared Error.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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Authors: A. Chellil, A. Nour, S. Lecheb, H. Mechakra, L. Addar, H. Kebir

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This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems.

Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: Aluminium alloys, plate, crack, failure.

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Authors: J. Davoodi , J. Moradi

Abstract:

The aim of this research was to calculate the mechanical properties of Pd3Rh and PdRh3 ordered alloys. The molecular dynamics (MD) simulation technique was used to obtain temperature dependence of the energy, the Yong modulus, the shear modulus, the bulk modulus, Poisson-s ratio and the elastic stiffness constants at the isobaric-isothermal (NPT) ensemble in the range of 100-325 K. The interatomic potential energy and force on atoms were calculated by Quantum Sutton-Chen (Q-SC) many body potential. Our MD simulation results show the effect of temperature on the cohesive energy and mechanical properties of Pd3Rh as well as PdRh3 alloys. Our computed results show good agreement with the experimental results where they have been available.

Keywords: Pd-Rh alloy; Mechanical properties; Moleculardynamics simulation

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Authors: M. A. Tayfun

Abstract:

Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves.

Keywords: Large waves, non-linear effects, simulation, spectra, spurious crests, Stokes waves, wave breaking, wave statistics.

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: Faris Elghaish, Sepehr Abrishami, Mark Gaterell, Richard Wise

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The collaboration and integration between all building information management (BIM) processes and tasks are necessary to ensure that all project objectives can be delivered. The literature review has been used to explore the state of the art BIM technologies to manage construction materials as well as the challenges which have faced the construction process using traditional methods. Thus, this paper aims to articulate a framework to integrate traditional material planning methods such as ABC analysis theory (Pareto principle) to analyse and categorise the project materials, as well as using independent material planning methods such as Economic Order Quantity (EOQ) and Fixed Order Point (FOP) into the BIM 4D, and 5D capabilities in order to articulate a dependent material planning cycle into BIM, which relies on the constructability method. Moreover, we build a model to connect between the material planning outputs and the BIM 4D and 5D data to ensure that all project information will be accurately presented throughout integrated and complementary BIM reporting formats. Furthermore, this paper will present a method to integrate between the risk management output and the material management process to ensure that all critical materials are monitored and managed under the all project stages. The paper includes browsers which are proposed to be embedded in any 4D BIM platform in order to predict the EOQ as well as FOP and alarm the user during the construction stage. This enables the planner to check the status of the materials on the site as well as to get alarm when the new order will be requested. Therefore, this will lead to manage all the project information in a single context and avoid missing any information at early design stage. Subsequently, the planner will be capable of building a more reliable 4D schedule by allocating the categorised material with the required EOQ to check the optimum locations for inventory and the temporary construction facilitates.

Keywords: Building information management, BIM, economic order quantity, fixed order point, BIM 4D, BIM 5D.

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Authors: N. Ould Cherchali, A. Tlemçani, M. S. Boucherit, A. Morsli

Abstract:

Nature-inspired metaheuristic algorithms, particularly those founded on swarm intelligence, have attracted much attention over the past decade. Firefly algorithm has appeared in approximately seven years ago, its literature has enlarged considerably with different applications. It is inspired by the behavior of fireflies. The aim of this paper is the application of firefly algorithm for solving a nonlinear algebraic system. This resolution is needed to study the Selective Harmonic Eliminated Pulse Width Modulation strategy (SHEPWM) to eliminate the low order harmonics; results have been applied on multilevel inverters. The final results from simulations indicate the elimination of the low order harmonics as desired. Finally, experimental results are presented to confirm the simulation results and validate the efficaciousness of the proposed approach.

Keywords: Firefly algorithm, metaheuristic algorithm, multilelvel inverter, SHEPWM.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

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This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Ameur Abdelkader, Abed Bouarfa Hafida

Abstract:

Since its inception, predictive analysis has revolutionized the IT industry through its robustness and decision-making facilities. It involves the application of a set of data processing techniques and algorithms in order to create predictive models. Its principle is based on finding relationships between explanatory variables and the predicted variables. Past occurrences are exploited to predict and to derive the unknown outcome. With the advent of big data, many studies have suggested the use of predictive analytics in order to process and analyze big data. Nevertheless, they have been curbed by the limits of classical methods of predictive analysis in case of a large amount of data. In fact, because of their volumes, their nature (semi or unstructured) and their variety, it is impossible to analyze efficiently big data via classical methods of predictive analysis. The authors attribute this weakness to the fact that predictive analysis algorithms do not allow the parallelization and distribution of calculation. In this paper, we propose to extend the predictive analysis algorithm, Classification And Regression Trees (CART), in order to adapt it for big data analysis. The major changes of this algorithm are presented and then a version of the extended algorithm is defined in order to make it applicable for a huge quantity of data.

Keywords: Predictive analysis, big data, predictive analysis algorithms. CART algorithm.

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Authors: Kashif Bilal, Tassawar Iqbal, Asad Ali Safi, Nadeem Daudpota

Abstract:

This paper deals with dynamic load balancing using PVM. In distributed environment Load Balancing and Heterogeneity are very critical issues and needed to drill down in order to achieve the optimal results and efficiency. Various techniques are being used in order to distribute the load dynamically among different nodes and to deal with heterogeneity. These techniques are using different approaches where Process Migration is basic concept with different optimal flavors. But Process Migration is not an easy job, it impose lot of burden and processing effort in order to track each process in nodes. We will propose a dynamic load balancing technique in which application will intelligently balance the load among different nodes, resulting in efficient use of system and have no overheads of process migration. It would also provide a simple solution to problem of load balancing in heterogeneous environment.

Keywords: PVM, load balancing, task allocation, intelligent application.

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Authors: K. V. Geetha, N. R. Mangalambal

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Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: Kiurski S. Jelena, Ranogajec G. Jonjaua, Kecić S. Vesna, Oros B. Ivana

Abstract:

The present study investigates the effectiveness of newly designed clayey pellets (fired clay pellets diameter sizes of 5 and 8 mm, and unfired clay pellets with the diameter size of 15 mm) as the beds in the column adsorption process. The adsorption experiments in the batch mode were performed before the column experiment with the purpose to determine the order of adsorbent package in the column which was to be designed in the investigation. The column experiment was performed by using a known mass of the clayey beds and the volume of the waste printing developer, which was purified. The column was filled in the following order: fired clay pellets of the diameter size of 5 mm, fired clay pellets of the diameter size of 8 mm, and unfired clay pellets of the diameter size of 15 mm. The selected order of the adsorbents showed a high removal efficiency for zinc (97.8%) and copper (81.5%) ions. These efficiencies were better than those in the case of the already existing mode adsorption. The obtained experimental data present a good basis for the selection of an appropriate column fill, but further testing is necessary in order to obtain more accurate results.

Keywords: Clay materials, fix bed adsorption column, metal ions, printing developer.

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Authors: Motahar Reza, Anadi Sankar Gupta

Abstract:

An analysis is made of the flow of an incompressible viscoelastic fluid (of small memory) over a porous plate subject to suction or blowing. It is found that velocity at a point increases with increase in the elasticity in the fluid. It is also shown that wall shear stress depends only on suction and is also independent of the material of fluids. No steady solution for velocity distribution exists when there is blowing at the plate. Temperature distribution in the boundary layer is determined and it is found that temperature at a point decreases with increase in the elasticity in the fluid.

Keywords: Viscoelastic fluid, Flow past a porous plate, Heat transfer

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Authors: A. Sohrabi

Abstract:

The importance of local food products and their promotion are drivers for economic growth. Entrepreneurship is one of the most important tools for development, which puts its most important effect on the way of increasing business in society. The purpose of this paper is to assess the breadth of food strategies in Italy toward to promoting local Italian foods in order to present useful food policies for developing countries. The methodology of this paper is based on qualitative analysis. In order to achieve such objectives, a literature review is carried out by employing documenting study. In this research, at first, we seek to present compliance’s concepts and definitions. Then, after examining the dimensions of the three strategies, we access to the indicators and compare their effects in order to present some useful policies and guidelines for developing countries. Despite of the limitations like inaccessibility, performance of companies in exporting local foods and lacking perception of awareness and experience of people, the study offers possible ways for future, as an example for Middle East countries to promote Italian local foods. The finding of this paper evaluates the three strategies in order to promote local food entrepreneurship in Italy and developing countries.

Keywords: Local food, Italian food, Italian strategy, food policy.

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Authors: E. Koyuncu

Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: Fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling.

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Authors: Duy Cuong Nguyen, Ali Makke, Guillaume Montay

Abstract:

This work presents an improved single fiber pull-out test for fiber/matrix interface characterization. This test has been used to study the Inter-Facial Shear Strength ‘IFSS’ of hemp fibers reinforced polypropylene (PP). For this aim, the fiber diameter has been carefully measured using a tomography inspired method. The fiber section contour can then be approximated by a circle or a polygon. The results show that the IFSS is overestimated if the circular approximation is used. The Influence of the molding temperature on the IFSS has also been studied. We find that a molding temperature of 183◦C leads to better interfacial properties. Above or below this temperature the interface strength is reduced.

Keywords: Interface, pull-out, processing, temperature, hemp, polypropylene, composite.

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Authors: Yani Rahmawati, Nadjadji Anwar, Christiono Utomo

Abstract:

Development in construction industry is leading to involve complexities in engineering systems; whereas it also required to its sustainability towards social, environmental, and economical aspects. Experts with requisite background and expertise are involved in order to integrate knowledge in achieving whole criteria through design process. Collaborative design is needed in order to attain optimum design through shared solution and goal from experts. This study is conducted to explore issues and approaches development of collaborative design research in construction and its influence to sustainability of the development. Literature review method is used in order to conceptually figure future research direction of collaborative design research. This research is a part of beginning process in doctoral research program, and will be used to support dissertation’s conceptual definition.

Keywords: Collaborative design, multi-discipline design, design process, sustainability of project development.

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Authors: S. Farzi

Abstract:

Recently, a lot of attention has been devoted to advanced techniques of system modeling. PNN(polynomial neural network) is a GMDH-type algorithm (Group Method of Data Handling) which is one of the useful method for modeling nonlinear systems but PNN performance depends strongly on the number of input variables and the order of polynomial which are determined by trial and error. In this paper, we introduce GPNN (genetic polynomial neural network) to improve the performance of PNN. GPNN determines the number of input variables and the order of all neurons with GA (genetic algorithm). We use GA to search between all possible values for the number of input variables and the order of polynomial. GPNN performance is obtained by two nonlinear systems. the quadratic equation and the time series Dow Jones stock index are two case studies for obtaining the GPNN performance.

Keywords: GMDH, GPNN, GA, PNN.

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Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

Abstract:

This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: Distributed model, flexible manipulator, observer, robot control.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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