Search results for: general solution

Authors: Y. Pala, M. O. Ertas

Abstract:

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

Procedia PDF Downloads 329

Authors: Alexander Matrosov, Guriy Shirunov

Abstract:

A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

Procedia PDF Downloads 571

Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

Abstract:

108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, since general theory of relativity has not given a quantitative solution to obscure and incorrect problems, generalization of gravitational theory has not been successfully completed yet although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore the obscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first step for achieving the purpose, the right solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometro dynamics, Schwarzschild, Poincaré

Procedia PDF Downloads 42

Authors: Saeed Otarod

Abstract:

In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

Procedia PDF Downloads 23

Authors: Mohsen Ziaee

Abstract:

Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

Procedia PDF Downloads 185

Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition

Procedia PDF Downloads 405

Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

Procedia PDF Downloads 191

Authors: Abdulrahman Abdulrahman

Abstract:

The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

Procedia PDF Downloads 174

Authors: Manana Chumburidze, David Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: the couple-stress thermoelasticity, boundary value problems, dynamic problems, approximate solution

Procedia PDF Downloads 485

Authors: Iyad M. Muslih, Yehya Abdellatif

Abstract:

In general, shading will reduce the electrical power produced from PV modules and arrays in locations where shading is unavoidable or caused by dynamic moving parts. This reduction is based on the shade effect on the I-V curve of the PV module or array and how the DC/AC inverter can search and control the optimum value of power from this module or array configuration. This is a very complicated task due to different patterns of shaded PV modules and arrays. One solution presented by the inverter industry is to perform the maximum power point tracking (MPPT) at the module level rather than the series string level. This solution is supposed to reduce the shade effect on the total harvested energy. However, this isn’t necessarily the best solution to reduce the shade effect as will be shown in this study.

Keywords: photovoltaic, shade effect, I-V curve, MPPT

Procedia PDF Downloads 376

Authors: Karim S. Hassan, Hisham M. Hamed, Yassmine A. Fahmy, Ahmed F. Shalash

Abstract:

The mismatch between in-phase and quadrature signals in Orthogonal frequency division multiplexing (OFDM) systems, such as DVB-T2, results in a severe degradation in performance. Several general solutions have been proposed in the past, but these are largely computationally intensive, leading to complex implementations. In this paper, we propose a relatively simple iterative solution, which provides good results in relatively few iterations, using fixed precision arithmetic. An additional advantage is that complex digital blocks, such as dividers and square root, are not required. Thus, the proposed solution may be implemented in relatively simple hardware.

Keywords: OFDM, DVB-T2, I/Q imbalance, I/Q mismatch, iterative method, fixed point, reduced complexity

Procedia PDF Downloads 514

Authors: T. A. Biala

Abstract:

This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process.

Keywords: linear multistep methods, boundary value methods, second order multipoint boundary value problems, convergence

Procedia PDF Downloads 355

Authors: Abdulrahman Abdulrahman

Abstract:

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

Keywords: analytical solution, combined channel, exponential channel, side weirs, trapezoidal channel, water surface profile

Procedia PDF Downloads 217

Authors: Ken Hampshire, Thomas Mazzuchi, Shahram Sarkani

Abstract:

As a subset of metaheuristics, nature-inspired optimization algorithms such as particle swarm optimization (PSO) have shown promise both in solving intractable problems and in their extensibility to novel problem formulations due to their general approach requiring few assumptions. Unfortunately, single instantiations of algorithms require detailed tuning of parameters and cannot be proven to be best suited to a particular illustrative problem on account of the “no free lunch” (NFL) theorem. Using these algorithms in real-world problems requires exquisite knowledge of the many techniques and is not conducive to reconciling the various approaches to given classes of problems. This research aims to present a unified view of PSO-based approaches from the perspective of relevant systems engineering problems, with the express purpose of then eliciting the best solution for any problem formulation in an ensemble learning bucket of models approach. The central hypothesis of the research is that extending the PSO algorithms found in the literature to real-world optimization problems requires a general ensemble-based method for all problem formulations but a specific implementation and solution for any instance. The main results are a problem-based literature survey and a general method to find more globally optimal solutions for any systems engineering optimization problem.

Keywords: particle swarm optimization, nature-inspired optimization, metaheuristics, systems engineering, ensemble learning

Procedia PDF Downloads 65

Authors: M.A.Bakry1, *, Aryn T. Shafeek1, +

Abstract:

In this article, absolute Parallelism geometry is used to study the torsional gravitational field. And discovered the tetrad fields, torsion vector, and torsion scalar of Schwarzschild space. The new solution of the torsional gravitational field is a generalization of Schwarzschild in the context of general relativity. The results are applied to the planetary orbits.

Keywords: absolute parallelism geometry, tetrad fields, torsion vectors, torsion scalar

Procedia PDF Downloads 120

Authors: Ahmed Khalil

Abstract:

Increased energy demands around the world have led to the raise in power production which has resulted with more greenhouse gas emissions through fossil sources. These fossil sources and emissions cause deterioration in echo-system. Therefore, renewable energy sources come to the scene as echo-friendly and clean energy sourcing, whereas the electrical devices and energy needs decrease in the timeline. Each of these renewable energy sources contribute to the reduction of greenhouse gases and mitigate environmental deterioration. However, there are also some general and source-specific challenges, which influence the choice of the investors. The most prominent general challenge that effects end-users’ comfort and reliability is usually determined as the intermittence which derives from the diversions of source conditions, due to nature dynamics and uncontrolled periodic changes. Research and development professionals strive to mitigate intermittence challenge through material improvement for each renewable source whereas hybrid source mix stand as a solution. This solution prevails well, when single renewable technologies are upgraded further. On the other hand, integration of energy efficient devices and systems, raise the affirmative effect of such solution in means of less energy requirement in sustainability composition or scenario. This paper provides a glimpse on the advantages of composing renewable source mix versus single usage, with contribution of sampled e-efficient systems and devices. Accordingly it demonstrates the extended benefits, through planning and predictive estimation stages of Ahmadi Town Projects in Kuwait.

Keywords: e-efficient systems, hybrid source, intermittence challenge, renewable energy

Procedia PDF Downloads 112

Authors: Gyo Woo Lee, Man Young Kim

Abstract:

The blocked-off formulations for the analysis of radiative heat transfer are formulated and examined in order to find the solutions in a two-dimensional complex enclosure. The final discretization equations using the step scheme for spatial differencing practice are proposed with the additional source term to incorporate the blocked-off procedure. After introducing the implementation for inactive region into the general discretization equation, three different problems are examined to find the performance of the solution methods.

Keywords: radiative heat transfer, Finite Volume Method (FVM), blocked-off solution procedure, body-fitted coordinate

Procedia PDF Downloads 270

Authors: Amir Mahmoudi

Abstract:

In this investigation, AISI321 steel after welding by Shilded Metal Arc Welding (SMAW) was solution heat treated in various temperatures and times, and then was sensitizied. Results indicated, increasing of temperature in solution heat treatment raises the sensitization and creates the cavity structure in grain boundaries. Besides, in order to examine the effect of time on solution heat treatment, all samples were solution heat treated at different times and fixed temperature (1050°C). By increasing the time, more chrome carbides were created due to dissolution of delta ferrite phase and reproduce titanium carbides. Additionally, the best process for solution heat treatment for this steel was suggested.

Keywords: stainless steel, solution heat treatment, intergranular corrosion, DLEPR

Procedia PDF Downloads 501

Authors: Nosakhare Enoma, Alphose Zingoni

Abstract:

The requirements for various toroidal shell forms are increasing due to new applications, available storage space and the consideration of appearance. Because of the complexity of some of these structural forms, the finite element method is nowadays mainly used for their analysis, even for simple static studies. This paper presents an easy-to-use analytical algorithm for pressurized multi-segmented toroidal shells of revolution. The membrane solution, which acts as a particular solution of the bending-theory equations, is developed based on membrane theory of shells, and a general approach is formulated for quantifying discontinuity effects at the shell junctions using the well-known Geckeler’s approximation. On superimposing these effects, and applying the ensuing solution to the problem of the pressurized toroid with four segments, closed-form stress results are obtained for the entire toroid. A numerical example is carried out using the developed method. The analytical results obtained show excellent agreement with those from the finite element method, indicating that the proposed method can be also used for complementing and verifying FEM results, and providing insights on other related problems.

Keywords: bending theory of shells, membrane hypothesis, pressurized toroid, segmented toroidal vessel, shell analysis

Procedia PDF Downloads 292

Authors: Mohammed Ali Hjaji, A.K. El-Senussi, Said H. Eshtewi

Abstract:

The flexural dynamic response of symmetric laminated composite beams subjected to general transverse harmonic forces is investigated. The dynamic equations of motion and associated boundary conditions based on the first order shear deformation are derived through the use of Hamilton’s principle. The influences of shear deformation, rotary inertia, Poisson’s ratio and fibre orientation are incorporated in the present formulation. The resulting governing flexural equations for symmetric composite Timoshenko beams are exactly solved and the closed form solutions for steady state flexural response are then obtained for cantilever and simply supported boundary conditions. The applicability of the analytical closed-form solution is demonstrated via several examples with various transverse harmonic loads and symmetric cross-ply and angle-ply laminates. Results based on the present solution are assessed and validated against other well established finite element solutions and exact solutions available in the literature.

Keywords: analytical solution, flexural response, harmonic forces, symmetric laminated beams, steady state response

Procedia PDF Downloads 463

Authors: Muhammad Umair, Yuri Nikolaev, Denis Artemov, Ighor Uzhinsky

Abstract:

A flexible manufacturing system is an integral part of a smart factory of industry 4.0 in which every machine is interconnected and works autonomously. Robots are in the process of replacing humans in every industrial sector. As the cyber-physical-system (CPS) and artificial intelligence (AI) are advancing, the manufacturing industry is getting more dependent on computers than human brains. This modernization has boosted the production with high quality and accuracy and shifted from classic production to smart manufacturing systems. However, material handling for such automated productions is a challenge and needs to be addressed with the best possible solution. Conventional clamping systems are designed for manual work and not suitable for highly automated production systems. Researchers and engineers are trying to find the most economical solution for loading/unloading and transportation workpieces from a warehouse to a machine shop for machining operations and back to the warehouse without human involvement. This work aims to propose an advanced multi-shape tooling solution for highly automated manufacturing systems. The currently obtained result shows that it could function well with automated guided vehicles (AGVs) and modern conveyor belts. The proposed solution is following requirements to be automation-friendly, universal for different part geometry and production operations. We used a bottom-up approach in this work, starting with studying different case scenarios and their limitations and finishing with the general solution.

Keywords: artificial intelligence, cyber physics system, Industry 4.0, material handling, smart factory, flexible manufacturing system

Procedia PDF Downloads 114

Authors: Mahmood Otadi, Maryam Mosleh

Abstract:

The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

Procedia PDF Downloads 489

Authors: K. S. Ghosh, Sagnik Bose, Kapil Tripati

Abstract:

Potentiodynamic polarization studies carried out on AA2024 and AA2014 Al-Cu-Mg alloys of various tempers in 3.5 wt. % NaCl and in 3.5 wt. % NaCl + 1.0 % H2O2 solution characteristic E-i curves. Corrosion potential (Ecorr) value has shifted towards more negative potential with the increase of artificial aging time. The Ecorr value for the alloy tempers has also shifted anodically in presence of H2O2 in 3.5 % NaCl solution. Further, passivity phenomenon has been observed in all the alloy tempers when tested in 3.5 wt. % NaCl solution at pH 12. Stress corrosion cracking (SCC) behaviour of friction stir weld (FSW) joint of AA2014 alloy has been studied bu slow strain rate test (SSRT) in 3.5 wt. % NaCl solution. Optical micrographs of the corroded surfaces of polarised samples showed general corrosion, extensive pitting and intergranular corrosion as well. Further, potentiodynamic cyclic polarization curves displayed wide hysteresis loop indicating that the alloy tempers are susceptible to pit growth damage. Attempts have been made to explain the variation of observed electrochemical and SCC behaviour of the alloy tempers and the electrolyte conditions with the help of microstructural features.

Keywords: AA 2014 and AA 2024 Al-C-Mg alloy, artificial ageing, potentiodynamic polarization, TEM micrographs, stress corrosion cracking (SCC)

Procedia PDF Downloads 305

Authors: Manuel Urueña Palomo

Abstract:

In this paper, we introduce the study of a new solution to gravitational singularities by violating the energy conditions of the Penrose Hawking singularity theorems. We consider that a shift to negative energies, and thus, to negative masses, takes place at the event horizon of a black hole, justified by the original, singular and exact Schwarzschild solution. These negative energies are supported by relativistic particle physics considering the negative energy solutions of the Dirac equation, which states that a time transformation shifts to a negative energy particle. In either general relativity or full Newtonian mechanics, these negative masses are predicted to be repulsive. It is demonstrated that the model fits actual observations, and could possibly clarify the size of observed and unexplained supermassive black holes, when considering the inflation that would take place inside the event horizon where massive particles interact antigravitationally. An approximated solution of the model proposed could be simulated in order to compare it with these observations.

Keywords: black holes, CPT symmetry, negative mass, time transformation

Procedia PDF Downloads 124

Authors: Agung Sujatmiko

Abstract:

One of the purposes of patent licensing was to transfer technology from developed countries to developing countries. For this reason, the role of the patent license agreement was very important and had a function as a tool to achieve technological development. This goal was very good, but in fact, many problems and obstacles arose in its implementation, so the technology transfer that had been implemented had not given good results. For this reason, it was necessary to find a solution so that technology could switch properly. The problem approach used the statutory and conceptual approaches. The analysis used was deductive by analyzing general laws and regulations and then concluding. Several regulations related to technology transfer were the main source to find answers to why technology transfer was difficult to achieve and what caused it. Once the cause was known, a solution would be sought.

Keywords: license, patent, technology, tie in clause

Procedia PDF Downloads 68

Authors: Hermanto J. M, Mirna Febriani

Abstract:

Resin acrylic, which is widely used, has the physical properties that can absorb liquids. This can lead to a change in the dimensions of the acrylic resin material. If repeated immersions were done, its strength would be affected. Disinfectant solutions have been widely used to reduce microorganisms both inside and outside the patient's mouth. One of the disinfecting materials that can be used is a clover solution. The purpose of this research is to find the ratio of water absorption of the acrylic resin material of self-cured type, soaked in clover solution for 10 minutes. The results showed that the average value obtained before soaked in clover solution was 0.0692 mg/cm3 and after soaked, in clover solution, the value was 0.090 mg/cm3. The conclusion of this research shows that the values of water sorption of acrylic resin before and after soaked in clover solution is still in ISO standard 1567/2001. Differences in water sorption value of self-cured acrylic resin before and after the immersion are caused by the process of liquid diffusion into the acrylic resin.

Keywords: absorption of fluid, self-cured acrylic resin, soaked, clover solution

Procedia PDF Downloads 142

Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

Abstract:

This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm

Procedia PDF Downloads 335

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

Procedia PDF Downloads 300

Authors: Zuhier Altawallbeh

Abstract:

This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

Procedia PDF Downloads 402

Authors: Hossein Kabir, Amir Hossein Hassanpour Mati-Kolaie

Abstract:

In the current study, the elastic field in an anisotropic elastic media is determined by implementing a general semi-analytical method. In this specific methodology, the displacement field is computed as a sum of finite functions with unknown coefficients. These aforementioned functions satisfy exactly both the homogeneous and inhomogeneous boundary conditions in the proposed media. It is worth mentioning that the unknown coefficients are determined by implementing the principle of minimum potential energy. The numerical integration is implemented by employing the Generalized Gaussian Quadrature solution. Furthermore, with the aid of the calculated unknown coefficients, the displacement field, as well as the other parameters of the elastic field, are obtainable as well. Finally, the comparison of the previous analytical method with the current semi-analytical method proposes the efficacy of the present methodology.

Keywords: anisotropic elastic media, semi-analytical method, elastic field, generalized gaussian quadrature solution

Procedia PDF Downloads 298