Search results for: Exact solution.

Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVP­s­) in ordinary differential equations (ODE­s­) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, First Order Ordinary Differential Equations, Hybrid, Self starting.

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Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: A. Amiri Delouei

Abstract:

In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: Functionally graded materials, unsteady heat conduction, cylinder, Temperature distribution.

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Authors: Elnaz Afshari, Siamak Najarian, Naser Simforoosh, Siamak Hajizadeh Farkoush

Abstract:

Minimally invasive surgery (MIS) is now being widely used as a preferred choice for various types of operations. The need to detect various tactile properties, justifies the key role of tactile sensing that is currently missing in MIS. In this regard, Laparoscopy is one of the methods of minimally invasive surgery that can be used in kidney stone removal surgeries. At this moment, determination of the exact location of stone during laparoscopy is one of the limitations of this method that no scientific solution has been found for so far. Artificial tactile sensing is a new method for obtaining the characteristics of a hard object embedded in a soft tissue. Artificial palpation is an important application of artificial tactile sensing that can be used in different types of surgeries. In this study, a new method for determining the exact location of stone during laparoscopy is presented. In the present study, the effects of stone existence on the surface of kidney were investigated using conceptual 3D model of kidney containing a simulated stone. Having imitated palpation and modeled it conceptually, indications of stone existence that appear on the surface of kidney were determined. A number of different cases were created and solved by the software and using stress distribution contours and stress graphs, it is illustrated that the created stress patterns on the surface of kidney show not only the existence of stone inside, but also its exact location. So three-dimensional analysis leads to a novel method of predicting the exact location of stone and can be directly applied to the incorporation of tactile sensing in artificial palpation, helping surgeons in non-invasive procedures.

Keywords: Kidney Stone, Laparoscopic Surgery, Artificial Tactile Sensing, Finite Element Method.

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Authors: Zhijie Ma, Qinglin Zhao, Hongning Dai, Huan Zhang

Abstract:

This paper proposes an APPLE scheme that aims at providing absolute and proportional throughput guarantees, and maximizing system throughput simultaneously for wireless LANs with homogeneous and heterogenous traffic. We formulate our objectives as an optimization problem, present its exact and approximate solutions, and prove the existence and uniqueness of the approximate solution. Simulations validate that APPLE scheme is accurate, and the approximate solution can well achieve the desired objectives already.

Keywords: IEEE 802.11e, throughput guarantee, priority.

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Authors: T. Zitoun, M. Bouhadef

Abstract:

When a partially or completely immersed solid moves in a liquid such as water, it undergoes a force called hydrodynamic drag. Reducing this force has always been the objective of hydrodynamic engineers to make water slide better on submerged bodies. This paper deals with the examination of the different terms composing the analytical solution of the flow over an obstacle embedded at the bottom of a hydraulic channel. We have chosen to use a linear method to study a two-dimensional flow over an obstacle, in order to understand the evolution of the drag. We set the following assumptions: incompressible inviscid fluid, irrotational flow, low obstacle height compared to the water height. Those assumptions allow overcoming the difficulties associated with modelling these waves. We will mathematically formulate the equations that allow the determination of the stream function, and then the free surface equation. A similar method is used to determine the exact analytical solution for an obstacle in the shape of a sinusoidal arch.

Keywords: Free-surface wave, inviscid fluid, analytical solution, hydraulic channel.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: Abbas Siefi, Mohammad Javad Karimifar

Abstract:

We study the spatial design of experiment and we want to select a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations and possibly at different times. In spatial design, when the design region and the set of interest are discrete then the covariance matrix completely describe any objective function and our goal is to choose a feasible design that minimizes the resulting uncertainty. The problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. This problem is NP-hard. For using these designs in computer experiments, in many cases, the design space is very large and it's not possible to calculate the exact optimal solution. Heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective and exact solution not possible. We developed a GA algorithm to take advantage of the exploratory power of this algorithm. The successful application of this method is demonstrated in large design space. We consider a real case of design of experiment. In our problem, design space is very large and for solving the problem, we used proposed GA algorithm.

Keywords: Spatial design of experiments, maximum entropy sampling, computer experiments, genetic algorithm.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented. The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm implementation for the control of a seven link (7 degrees of freedom, 7DOF) manipulator are given.

Keywords: Manipulator, trajectory planning, unknown obstacles

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Authors: Mahmoud Zarrini, Sanaz Torkaman

Abstract:

In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

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Authors: Fatih Kara, Cabir Vural

Abstract:

In this work, a special case of the image superresolution problem where the only type of motion is global translational motion and the blurs are shift-invariant is investigated. The necessary conditions for exact reconstruction of the original image by using finite impulse-response reconstruction filters are developed. Given that the conditions are satisfied, a method for exact super-resolution is presented and some simulation results are shown.

Keywords: Image processing, image super-resolution, finite impulse-response filters, existence-uniqueness conditions.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

Abstract:

A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

Abstract:

The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: Rado Flajs, Miran Saje

Abstract:

We present a simple nonconforming approximation of the linear two–point boundary value problem which violates patch test requirements. Nevertheless the solutions, obtained from these type of approximations, converge to the exact solution.

Keywords: Generalized patch test, Irons' patch test, nonconforming finite element, convergence.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Chien-Chun Kung, Feng-Lung Chiang, Kuei-Yi Chen

Abstract:

In this paper, we will implement three-dimensional pursuit guidance law with feedback linearization control method and study the effects of parameters. First, we introduce guidance laws and equations of motion of a missile. Pursuit guidance law is our highlight. We apply feedback linearization control method to obtain the accelerations to implement pursuit guidance law. The solution makes warhead direction follow with line-of-sight. Final, the simulation results show that the exact solution derived in this paper is correct and some factors e.g. control gain, time delay, are important to implement pursuit guidance law.

Keywords: Pursuit guidance law, feedback linearization.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: S. Kavitha, Nirmala P. Ratchagar

Abstract:

This paper presents the novel deterministic dynamic programming approach for solving optimization problem with quadratic objective function with linear equality and inequality constraints. The proposed method employs backward recursion in which computations proceeds from last stage to first stage in a multi-stage decision problem. A generalized recursive equation which gives the exact solution of an optimization problem is derived in this paper. The method is purely analytical and avoids the usage of initial solution. The feasibility of the proposed method is demonstrated with a practical example. The numerical results show that the proposed method provides global optimum solution with negligible computation time.

Keywords: Backward recursion, Dynamic programming, Multi-stage decision problem, Quadratic objective function.

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Authors: Bubaker M. F. Bushofa, Abdel Hafez A. Azab

Abstract:

This article is based on the technique which is called Discrete Parameter Tracking (DPT). First introduced by A. A. Azab [8] which is applicable for less order reference model. The order of the reference model is (n-l) and n is the number of the adjustable parameters in the physical plant. The technique utilizes a modified gradient method [9] where the knowledge of the exact order of the nonadaptive system is not required, so, as to eliminate the identification problem. The applicability of the mentioned technique (DPT) was examined through the solution of several problems. This article introduces the solution of a third order system with three adjustable parameters, controlled according to second order reference model. The adjustable parameters have great initial error which represent condition. Computer simulations for the solution and analysis are provided to demonstrate the simplicity and feasibility of the technique.

Keywords: Adaptive Control System, Discrete Parameter Tracking, Discrete Time Model.

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Authors: Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib

Abstract:

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating  that the flow equations possess an infinite set of solutions. 

Keywords: Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows

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Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue

Abstract:

A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.

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Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Anupma Bansal

Abstract:

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions

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Authors: A. M. Sagir

Abstract:

In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Praveen Saraswat, Vipin Kumar Verma, Rudraman Singh

Abstract:

The unsteady transient free convection flow of an incompressible dissipative viscous fluid between parallel plates at different distances have been investigated under porous medium. Due to presence of heat flux under the influence of uniform transverse magnetic field the velocity distribution and the temperature distribution, is shown graphically. Since exact solution is not possible so we find parametrical solution by perturbation technique. The result is shown in graph for different parameters. We notice that heat generation effects fluid velocity keeping in which of free convection which cools.

Keywords: Transient, Convection, MHD, Viscous, Porous.

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

Abstract:

Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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Authors: Praveen Saraswat, Rudraman Singh

Abstract:

In this paper, we have investigated the free convection MHD flow due to heat and mass transfer through porous medium bounded by an infinite vertical non-conducting porous plate with time dependent suction under the influence of uniform transverse magnetic field of strength H₀. When Temperature (T) and Concentration (C) at the plate is oscillatory with time about a constant non-zero mean. The velocity distribution, the temperature distribution, co-efficient of skin friction and role of heat transfer is investigated. Here the partial differential equations are involved. Exact solution is not possible so approximate solution is obtained and various graphs are plotted.

Keywords: Time Dependent Suction, Convection, MHD, Porous.

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Authors: T. Cornelius

Abstract:

Masonry cavity walls are loaded by wind pressure and vertical load from upper floors. These loads results in bending moments and compression forces in the ties connecting the outer and the inner wall in a cavity wall. Large cavity walls are furthermore loaded by differential movements from the temperature gradient between the outer and the inner wall, which results in critical increase of the bending moments in the ties. Since the ties are loaded by combined compression and moment forces, the loadbearing capacity is derived from instability equilibrium equations. Most of them are iterative, since exact instability solutions are complex to derive, not to mention the extra complexity introducing dimensional instability from the temperature gradients. Using an inverse variable substitution and comparing an exact theory with an analytical instability solution a method to design tie-connectors in cavity walls was developed. The method takes into account constraint conditions limiting the free length of the wall tie, and the instability in case of pure compression which gives an optimal load bearing capacity. The model is illustrated with examples from praxis.

Keywords: Masonry, tie connectors, cavity wall, instability, differential movements, combined bending and compression.

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Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: R. K. Dubey

Abstract:

Bianchi type cosmological models have been studied on the basis of Lyra’s geometry. Exact solution has been obtained by considering a time dependent displacement field for constant deceleration parameter and varying cosmological term of the universe. The physical behavior of the different models has been examined for different cases.

Keywords: Bianchi type-I cosmological model, variable gravitational coupling (G) and Cosmological Constant term (β).

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