Search results for: SSS equation.
1032 New Fourth Order Explicit Group Method in the Solution of the Helmholtz Equation
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20711031 A Modified Laplace Decomposition Algorithm Solution for Blasius’ Boundary Layer Equation of the Flat Plate in a Uniform Stream
Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh
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In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.
Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23651030 Analytical Solutions of Kortweg-de Vries(KdV) Equation
Authors: Foad Saadi, M. Jalali Azizpour, S.A. Zahedi
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The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.Keywords: Variational Iteration Method (VIM), HomotopyPerturbation Method (HPM), Homotopy Analysis Method (HAM), KdV Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23601029 The Dividend Payments for General Claim Size Distributions under Interest Rate
Authors: Li-Li Li, Jinghai Feng, Lixin Song
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This paper evaluates the dividend payments for general claim size distributions in the presence of a dividend barrier. The surplus of a company is modeled using the classical risk process perturbed by diffusion, and in addition, it is assumed to accrue interest at a constant rate. After presenting the integro-differential equation with initial conditions that dividend payments satisfies, the paper derives a useful expression of the dividend payments by employing the theory of Volterra equation. Furthermore, the optimal value of dividend barrier is found. Finally, numerical examples illustrate the optimality of optimal dividend barrier and the effects of parameters on dividend payments.Keywords: Dividend payout, Integro-differential equation, Jumpdiffusion model, Volterra equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17861028 Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation
Authors: G.Hariharan, K.Kannan
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In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.
Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27671027 Mathematical Modelling of Transport Phenomena in Radioactive Waste-Cement-Bentonite Matrix
Authors: Ilija Plecas, Uranija Kozmidis-Luburic, Radojica Pesic
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The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.
Keywords: bentonite, cement , radioactive waste, composite, disposal, diffusion
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22781026 Stability Analysis of Two-delay Differential Equation for Parkinson's Disease Models with Positive Feedback
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6471025 Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation
Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey
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In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13561024 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide
Authors: Arti Vaish, Harish Parthasarathy
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In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16881023 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning
Authors: Azita Tajaddini, Ramleh Shamsi
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In this paper, we present the block generalized minimal residual (BGMRES) method in order to solve the generalized Sylvester matrix equation. However, this method may not be converged in some problems. We construct a polynomial preconditioner based on BGMRES which shows why polynomial preconditioner is superior to some block solvers. Finally, numerical experiments report the effectiveness of this method.Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8621022 On the Existence and Global Attractivity of Solutions of a Functional Integral Equation
Authors: Asadollah Aghajani, Yaghoub Jalilian
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Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.
Keywords: Functional integral equation, fixed-point, measure of noncompactness, attractive solution, asymptotic stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12441021 Assessment of Hargreaves Equation for Estimating Monthly Reference Evapotranspiration in the South of Iran
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, FAOPenman method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18991020 On CR-Structure and F-Structure Satisfying Polynomial Equation
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7821019 Solving Inhomogeneous Wave Equation Cauchy Problems using Homotopy Perturbation Method
Authors: Mohamed M. Mousa, Aidarkhan Kaltayev
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In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).
Keywords: Homotopy perturbation method, Exact solution, Cauchy problem, inhomogeneous wave equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17971018 Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation
Authors: Kew Lee Ming, Norhashidah Hj. Mohd. Ali
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In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.Keywords: Telegraph equation, explicit group iterative scheme, domain decomposition algorithm, parallelization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15151017 Modeling and Numerical Simulation of Sound Radiation by the Boundary Element Method
Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.
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The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.
Keywords: Acoustic radiation, boundary element
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14631016 Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method
Authors: Ou Xie, Zhenyu Zhao
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In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.
Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14401015 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming
Authors: N. Kumaresan, J. Kavikumar, M. Kumudthaa, Kuru Ratnavelu
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In this paper, solution of fuzzy differential equation under general differentiability is obtained by genetic programming (GP). The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.Keywords: Fuzzy differential equation, Generalized differentiability, Genetic programming and H-difference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22311014 A Schur Method for Solving Projected Continuous-Time Sylvester Equations
Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou
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In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18101013 Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation
Authors: Kelong Zheng, Jinsong Hu,
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In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.
Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18481012 Stability of Stochastic Model Predictive Control for Schrödinger Equation with Finite Approximation
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23321011 Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4231010 Complex Fuzzy Evolution Equation with Nonlocal Conditions
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10371009 An Asymptotic Solution for the Free Boundary Parabolic Equations
Authors: Hsuan-Ku Liu, Ming Long Liu
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In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.
Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14631008 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25921007 Periodic Solutions for a Higher Order Nonlinear Neutral Functional Differential Equation
Authors: Yanling Zhu
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In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.
Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12571006 Optimal Relaxation Parameters for Obtaining Efficient Iterative Methods for the Solution of Electromagnetic Scattering Problems
Authors: Nadaniela Egidi, Pierluigi Maponi
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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.
Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1731005 An H1-Galerkin Mixed Method for the Coupled Burgers Equation
Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang
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In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.
Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15411004 An Examination and Validation of the Theoretical Resistivity-Temperature Relationship for Conductors
Authors: Fred Lacy
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Electrical resistivity is a fundamental parameter of metals or electrical conductors. Since resistivity is a function of temperature, in order to completely understand the behavior of metals, a temperature dependent theoretical model is needed. A model based on physics principles has recently been developed to obtain an equation that relates electrical resistivity to temperature. This equation is dependent upon a parameter associated with the electron travel time before being scattered, and a parameter that relates the energy of the atoms and their separation distance. Analysis of the energy parameter reveals that the equation is optimized if the proportionality term in the equation is not constant but varies over the temperature range. Additional analysis reveals that the theoretical equation can be used to determine the mean free path of conduction electrons, the number of defects in the atomic lattice, and the ‘equivalent’ charge associated with the metallic bonding of the atoms. All of this analysis provides validation for the theoretical model and provides insight into the behavior of metals where performance is affected by temperatures (e.g., integrated circuits and temperature sensors).
Keywords: Callendar–van Dusen, conductivity, mean free path, resistance temperature detector, temperature sensor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21731003 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation
Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail
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In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1889