Search results for: system of Diophantine equations and calculus.

Authors: Xun Ge, Jingju Qian

Abstract:

To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, higher mathematics scores, decision attribute, condition attribute.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1052

Authors: Li Zong-Cheng

Abstract:

It is by reason of the unified measure of varieties of resources and the unified processing of the disposal of varieties of resources, that these closely related three of new basic models called the resources assembled node and the disposition integrated node as well as the intelligent organizing node are put forth in this paper; the three closely related quantities of integrative analytical mechanics including the disposal intensity and disposal- weighted intensity as well as the charge of resource charge are set; and then the resources assembled space and the disposition integrated space as well as the intelligent organizing space are put forth. The system of fundamental equations and model of complete factor synergetics is preliminarily approached for the general situation in this paper, to form the analytical base of complete factor synergetics. By the essential variables constituting this system of equations we should set twenty variables respectively with relation to the essential dynamical effect, external synergetic action and internal synergetic action of the system.

Keywords: complex system, disposal of resources, completefactor synergetics, fundamental equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1385

Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1135

Authors: Corneliu Sofronie, Roxana Zubcov

Abstract:

Cognitive Science appeared about 40 years ago, subsequent to the challenge of the Artificial Intelligence, as common territory for several scientific disciplines such as: IT, mathematics, psychology, neurology, philosophy, sociology, and linguistics. The new born science was justified by the complexity of the problems related to the human knowledge on one hand, and on the other by the fact that none of the above mentioned sciences could explain alone the mental phenomena. Based on the data supplied by the experimental sciences such as psychology or neurology, models of the human mind operation are built in the cognition science. These models are implemented in computer programs and/or electronic circuits (specific to the artificial intelligence) – cognitive systems – whose competences and performances are compared to the human ones, leading to the psychology and neurology data reinterpretation, respectively to the construction of new models. During these processes if psychology provides the experimental basis, philosophy and mathematics provides the abstraction level utterly necessary for the intermission of the mentioned sciences. The ongoing general problematic of the cognitive approach provides two important types of approach: the computational one, starting from the idea that the mental phenomenon can be reduced to 1 and 0 type calculus operations, and the connection one that considers the thinking products as being a result of the interaction between all the composing (included) systems. In the field of psychology measurements in the computational register use classical inquiries and psychometrical tests, generally based on calculus methods. Deeming things from both sides that are representing the cognitive science, we can notice a gap in psychological product measurement possibilities, regarded from the connectionist perspective, that requires the unitary understanding of the quality – quantity whole. In such approach measurement by calculus proves to be inefficient. Our researches, deployed for longer than 20 years, lead to the conclusion that measuring by forms properly fits to the connectionism laws and principles.

Keywords: complementary methodology, connection approach, networks without scaling, quantum psychology.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3550

Authors: M. Ndaw, G. Mendy, S. Ouya

Abstract:

Information system risk management helps to reduce or eliminate risk by implementing appropriate controls. In this paper, we propose a quantification model of controls impact on information system risks by automatizing the residual criticality estimation step of FMECA which is based on a inductive reasoning. For this, we defined three equations based on type and maturity of controls. For testing, the values obtained with the model were compared to estimated values given by interlocutors during different working sessions and the result is satisfactory. This model allows an optimal assessment of controls maturity and facilitates risk analysis of information system.

Keywords: Information System, Risk, Control, FMECA.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1531

Authors: S.C. Swain, S. Panda, A.K. Mohanty, C. Ardil

Abstract:

This paper presents the applications of computational intelligence techniques to economic load dispatch problems. The fuel cost equation of a thermal plant is generally expressed as continuous quadratic equation. In real situations the fuel cost equations can be discontinuous. In view of the above, both continuous and discontinuous fuel cost equations are considered in the present paper. First, genetic algorithm optimization technique is applied to a 6- generator 26-bus test system having continuous fuel cost equations. Results are compared to conventional quadratic programming method to show the superiority of the proposed computational intelligence technique. Further, a 10-generator system each with three fuel options distributed in three areas is considered and particle swarm optimization algorithm is employed to minimize the cost of generation. To show the superiority of the proposed approach, the results are compared with other published methods.

Keywords: Economic Load Dispatch, Continuous Fuel Cost, Quadratic Programming, Real-Coded Genetic Algorithm, Discontinuous Fuel Cost, Particle Swarm Optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2240

Authors: Gilberto Gonzalez-A, Ignacio Rodríguez- A., Dunia Nuñez-P

Abstract:

A bond graph model of a two degrees of freedom PUMA is described. System inversion gives the system input required to generate a given system output. In order to get the system inversion of the PUMA manipulator, a linearization of the nonlinear bond graph is obtained. Hence, the bicausality of the linearized bond graph of the PUMA manipulator is applied. Thus, the bicausal bond graph provides a systematic way of generating the equations of the system inversion. Simulation results to verify the calculated input for a given output are shown.

Keywords: Bond graph, system inversion, bicausality, PUMA manipulator

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1970

Authors: Adam L. Yanagihara, Yong Seok Park

Abstract:

The goal of this paper is to converge upon a design of a brake system that could be used for a roller coaster found at an amusement park. It was necessary to find what could be deemed as a “comfortable” deceleration so that passengers do not feel as if they are suddenly jerked and pressed against the restraining harnesses. A human factors engineering approach was taken in order to determine this deceleration. Using a previous study that tested the deceleration of transit vehicles, it was found that a -0.45 G deceleration would be used as a design requirement to build this system around. An adjustable linear eddy current brake using permanent magnets would be the ideal system to use in order to meet this design requirement. Anthropometric data were then used to determine a realistic weight and length of the roller coaster that the brake was being designed for. The weight and length data were then factored into magnetic brake force equations. These equations were used to determine how the brake system and the brake run layout would be designed. A final design for the brake was determined and it was found that a total of 12 brakes would be needed with a maximum braking distance of 53.6 m in order to stop a roller coaster travelling at its top speed and loaded to maximum capacity. This design is derived from theoretical calculations, but is within the realm of feasibility.

Keywords: Eddy current brake, engineering design, human factors engineering.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1096

Authors: Geeta Partap, Nitika Chugh

Abstract:

The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: Microstretch, deflection, exponential load, Laplace transforms, Residue theorem, simply supported.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 897

Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1968

Authors: C. Recommandé, J.C. Blind, A. Clavel, R. Gourichon, V. Le Gal

Abstract:

Simulations are developed in this paper with usual DSGE model equations. The model is based on simplified version of Smets-Wouters equations in use at European Central Bank which implies 10 macro-economic variables: consumption, investment, wages, inflation, capital stock, interest rates, production, capital accumulation, labour and credit rate, and allows take into consideration the banking system. Throughout the simulations, this model will be used to evaluate the impact of rate shocks recounting the actions of the European Central Bank during 2008.

Keywords: CC-LM, Central Bank, DSGE, Liquidity Shock, Non-standard Intervention.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1883

Authors: Ibrahim Abu-Alshaikh

Abstract:

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1646

Authors: Alireza Fereidooni, Kamran Behdinan, Zouheir Fawaz

Abstract:

The integral form of equations of motion of composite beams subjected to varying time loads are discretized using a developed finite element model. The model consists of a straight five node twenty-two degrees of freedom beam element. The stability analysis of the beams is studied by solving the matrix form characteristic equations of the system. The principle of virtual work and the first order shear deformation theory are employed to analyze the beams with large deformation and small strains. The regions of dynamic instability of the beam are determined by solving the obtained Mathieu form of differential equations. The effects of nonconservative loads, shear stiffness, and damping parameters on stability and response of the beams are examined. Several numerical calculations are presented to compare the results with data reported by other researchers.

Keywords: Finite element beam model, Composite Beams, stability analysis

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2180

Authors: M. Alrasheedi

Abstract:

The double exponential model (DEM), or Laplace distribution, is used in various disciplines. However, there are issues related to the construction of confidence intervals (CI), when using the distribution.In this paper, the properties of DEM are considered with intention of constructing CI based on simulated data. The analysis of pivotal equations for the models here in comparisons with pivotal equations for normal distribution are performed, and the results obtained from simulation data are presented.

Keywords: Confidence intervals, double exponential model, pivotal equations, simulation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3515

Authors: Arun Goel

Abstract:

Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly & Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly & Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicate the improvement in the performance of SVM (Poly & Rbf) in comparison to dimensional form of scour.

Keywords: Modeling, pier scour, regression, prediction, SVM (Poly & Rbf kernels).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1508

Authors: Pan Cheng, Jin Huang, Guang Zeng

Abstract:

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.

Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3607

Authors: G. Zahedi, H. Yaghoobi

Abstract:

Modeling of a heterogeneous industrial fixed bed reactor for selective dehydrogenation of heavy paraffin with Pt-Sn- Al2O3 catalyst has been the subject of current study. By applying mass balance, momentum balance for appropriate element of reactor and using pressure drop, rate and deactivation equations, a detailed model of the reactor has been obtained. Mass balance equations have been written for five different components. In order to estimate reactor production by the passage of time, the reactor model which is a set of partial differential equations, ordinary differential equations and algebraic equations has been solved numerically. Paraffins, olefins, dienes, aromatics and hydrogen mole percent as a function of time and reactor radius have been found by numerical solution of the model. Results of model have been compared with industrial reactor data at different operation times. The comparison successfully confirms validity of proposed model.

Keywords: Dehydrogenation, fixed bed reactor, modeling, linear alkyl benzene.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2987

Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

Abstract:

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1449

Authors: Alireza Abbasi Moshaii, Mehdi Tale Masouleh, Esmail Zarezadeh, Kamran Farajzadeh

Abstract:

The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3- RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. A mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, the CAD model of these robots has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: Robotic, Static analysis, 3-RCC, 3-RRS.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1926

Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1627

Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1265

Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: Integral images, differential images, differential filters, image fusion.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2052

Authors: Carmen Navarrete, Eloy Anguiano

Abstract:

In the last years, the computers have increased their capacity of calculus and networks, for the interconnection of these machines. The networks have been improved until obtaining the actual high rates of data transferring. The programs that nowadays try to take advantage of these new technologies cannot be written using the traditional techniques of programming, since most of the algorithms were designed for being executed in an only processor,in a nonconcurrent form instead of being executed concurrently ina set of processors working and communicating through a network.This paper aims to present the ongoing development of a new system for the reconfiguration of grouping of computers, taking into account these new technologies.

Keywords: Dynamic network topology, resource and task allocation, parallel computing, heterogeneous computing, dynamic reconfiguration.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1330

Authors: Samina Elyas Mubeen, R. K. Nema, Gayatri Agnihotri

Abstract:

In this paper the performance of unified power flow controller is investigated in controlling the flow of po wer over the transmission line. Voltage sources model is utilized to study the behaviour of the UPFC in regulating the active, reactive power and voltage profile. This model is incorporated in Newton Raphson algorithm for load flow studies. Simultaneous method is employed in which equations of UPFC and the power balance equations of network are combined in to one set of non-linear algebraic equations. It is solved according to the Newton raphson algorithm. Case studies are carried on standard 5 bus network. Simulation is done in Matlab. The result of network with and without using UPFC are compared in terms of active and reactive power flows in the line and active and reactive power flows at the bus to analyze the performance of UPFC.

Keywords: Newton-Raphson algorithm, Load flow, Unified power flow controller, Voltage source model.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4245

Authors: Osama Yusuf Ababneh

Abstract:

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

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2918

Authors: Z.D. Yang, E.S.S. Lam

Abstract:

Considering the merits and limitations of energy dissipation system, seismic isolation system and suspension system, a new earthquake resistant system is proposed and is demonstrated numerically through a frame-core structure. Base isolators and story isolators are installed in the proposed system. The former “isolates" the frame from the foundation and the latter “separates" the frame from the center core. Equations of motion are formulated to study the response of the proposed structural system to strong earthquake motion. As compared with the fixed-base building system, the proposed structural system shows substantial reduction on structural response.

Keywords: Base Isolator, Core-tube, Isolated frame, Seismic Mitigation, Story Isolator

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1986

Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1620

Authors: M. Faraji, F. Berroug

Abstract:

A one-dimensional mathematical model was developed in order to analyze and optimize the latent heat storage wall. The governing equations for energy transport were developed by using the enthalpy method and discretized with volume control scheme. The resulting algebraic equations were next solved iteratively by using TDMA algorithm. A series of numerical investigations were conducted in order to examine the effects of the thickness of the PCM layer on the thermal behavior of the proposed heating system. Results are obtained for thermal gain and temperature fluctuation. The charging discharging process was also presented and analyzed.

Keywords: Phase change material, Building, Concrete, Latent heat, Thermal control.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2108

Authors: Arti Vaish, Harish Parthasarathy

Abstract:

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1621

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

Abstract:

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

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 610