Search results for: coupled parabolic hyperbolic system

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

Abstract:

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

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1556

Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1502

Authors: M. A. Beisenbi, N. M. Kissikova, S. E. Beisembina, S. T. Suleimenova, S. A. Kaliyeva

Abstract:

The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector-functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: Gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 459

Authors: Avadhesh Yadav, Manoj Kumar, Balram

Abstract:

A solar powered air heating system using parabolic trough collector was experimentally investigated. In this experimental setup, the reflected solar radiations were focused on absorber tube which was placed at focal length of the parabolic trough. In this setup, air was used as working fluid which collects the heat from absorber tube. To enhance the performance of parabolic trough, collector with different type of reflectors were used. It was observed For Aluminum sheet maximum temperature is 52.3ºC, which 24.22% more than steel sheet as reflector and 8.5% more than Aluminum foil as reflector, also efficiency by using Aluminum sheet as reflector compared to steel sheet as reflector is 61.18% more. Efficiency by using Aluminum sheet as reflector compared to Aluminum foil as reflector is 18.98% more.

Keywords: Parabolic trough collector, Reflectors, Air flow rates.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4990

Authors: Basri Çelik

Abstract:

In this paper, the notion of Hyperbolic Klingenberg plane is introduced via a set of axioms like as Affine Klingenberg planes and Projective Klingenberg planes. Models of such planes are constructed by deleting a certain number m of equivalence classes of lines from a Projective Klingenberg plane. In the finite case, an upper bound for m is established and some combinatoric properties are investigated.

Keywords: Hyperbolic planes, Klingenberg planes, Projective planes.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1328

Authors: Gozel Judakova, Markus Bause

Abstract:

We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: Discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, two-phase flow.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 790

Authors: Shiping Zhou, Minggen Cui

Abstract:

This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1580

Authors: A. A. Penin

Abstract:

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

Keywords: a solar cell generator, I − V characteristic, p − n junction, approximation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1418

Authors: Rohit Tripathi, Sumit Tiwari, G. N. Tiwari

Abstract:

In present study, an approach is adopted where photovoltaic thermal flat plate collector is integrated with compound parabolic concentrator. Analytical expression of temperature dependent electrical efficiency of N number of partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) water collector connected in series has been derived with the help of basic thermal energy balance equations. Analysis has been carried for winter weather condition at Delhi location, India. Energy and exergy performance of N - partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) Water collector system has been compared for two cases: (i) 25% area of water collector covered by PV module, (ii) 75% area of water collector covered by PV module. It is observed that case (i) has been best suited for thermal performance and case (ii) for electrical energy as well as overall exergy.

Keywords: Compound parabolic concentrator, Energy, Photovoltaic thermal, Temperature dependent electrical efficiency.

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

Authors: Jinfeng Wang, Yang Liu, Hong Li

Abstract:

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2137

Authors: Angela Unna Chukwu, Samuel Oluwafemi Oyamakin

Abstract:

We proposed a Hyperbolic Gompertz Growth Model (HGGM), which was developed by introducing a shape parameter (allometric). This was achieved by convoluting hyperbolic sine function on the intrinsic rate of growth in the classical gompertz growth equation. The resulting integral solution obtained deterministically was reprogrammed into a statistical model and used in modeling the height and diameter of Pines (Pinus caribaea). Its ability in model prediction was compared with the classical gompertz growth model, an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while the independence of the error term was confirmed using the runs test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic gompertz growth models better than the source model (classical gompertz growth model) while the results of R2, Adj. R2, MSE and AIC confirmed the predictive power of the Hyperbolic Gompertz growth models over its source model.

Keywords: Height, Dbh, forest, Pinus caribaea, hyperbolic, gompertz.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2707

Authors: M. M. Isa, R. Abd-Rahman, H. H. Goh

Abstract:

A compound parabolic concentrator (CPC) is a wellknown non-imaging concentrator that will concentrate the solar radiation onto receiver (PV cell). One of disadvantage of CPC is has tall and narrow height compared to its diameter entry aperture area. Therefore, for economic reason, a truncation had been done by removed from the top of the full height CPC. This also will lead to the decreases of concentration ratio but it will be negligible. In this paper, the flux distribution of untruncated and truncated 2-D hollow compound parabolic trough concentrator (hCPTC) design is presented. The untruncated design has initial height H=193.4mm with concentration ratio C_(2-D)=4. This paper presents the optical simulation of compound parabolic trough concentrator using raytracing software TracePro. Results showed that, after the truncation, the height of CPC reduced 45% from initial height with the geometrical concentration ratio only decrease 10%. Thus, the cost of reflector and material dielectric usage can be saved especially at manufacturing site.

Keywords: Compound parabolic trough concentrator, optical modelling, ray-tracing analysis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3340

Authors: S. N. Vijayan, S. Sendhil Kumar

Abstract:

Recent years have an upward trend in the research of renewable energy sector, due to the low availability of resources and huge consumption of conventional energies. Considerable renewable energy can be achieved from the available solar power with the utilization of collecting systems. Parabolic trough concentrating collector systems are mostly used to utilize maximum availability of solar power. This paper reviews the contributing factors for the overall performance of parabolic trough collectors. Its performance depends on the operating parameters such as the type of receiver and the collector material, medium of heat transfer, type of application and various climatic conditions.

Keywords: Solar radiation, parabolic trough collector, thermal analysis, efficiency.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1020

Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

Abstract:

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 1369

Authors: E. Asadzadeh, M. Alam

Abstract:

This study offers a comprehensive review of the research papers published in the field of cooling towers and gives an insight into the latest developments of the natural draught cooling towers. Different modeling, analysis and design techniques are summarized and the challenges are discussed. The 118 references included in this paper are mostly concentrated on the review of the published papers after 2005. The present paper represents a complete collection of the studies done for cooling towers and would give an updated material for the researchers and design engineers in the field of hyperbolic cooling towers.

Keywords: Hyperbolic cooling towers, earthquakes, wind, nonlinear behavior, buckling, collapse, interference.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3987

Authors: Hyoup-Sang Yoon

Abstract:

Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.

Keywords: VOD, CDN, parabolic fractal distribution, viewing rank, weighted linear model fitting

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1790

Authors: Oladeinde Mobolaji Humphrey, Akpobi John

Abstract:

A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2083

Authors: Jingbo Yang, Hong Li, Yang Liu, Siriguleng He

Abstract:

In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.

Keywords: Pseudo-hyperbolic partial integro-differential equations, Nonconforming mixed element method, Semilinear, Error estimates.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1640

Authors: Esmaeil Asadzadeh, Mehtab Alam

Abstract:

Progressive collapse of the layered hyperbolic tower shells are studied considering the influences of changes in the supporting columns’ types and angles. 3-D time history analyses employing the finite element method are performed for the towers supported with I-type and ᴧ-type column. It is found that the inclination angle of the supporting columns is a very important parameter in optimization and safe design of the cooling towers against the progressive collapse. It is also concluded that use of Demand Capacity Ratio (DCR) criteria of the linear elastic approach recommended by GSA is un-conservative for the hyperbolic tower shells.

Keywords: Progressive collapse, cooling towers, finite element analysis, crack generation, reinforced concrete.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1355

Authors: Defne Akay, Bekir S. Kandemir

Abstract:

In this paper, we investigate the low-lying energy levels of the two-dimensional parabolic graphene quantum dots (GQDs) in the presence of topological defects with long range Coulomb impurity and subjected to an external uniform magnetic field. The low-lying energy levels of the system are obtained within the framework of the perturbation theory. We theoretically demonstrate that a valley splitting can be controlled by geometrical parameters of the graphene quantum dots and/or by tuning a uniform magnetic field, as well as topological defects. It is found that, for parabolic graphene dots, the valley splitting occurs due to the introduction of spatial confinement. The corresponding splitting is enhanced by the introduction of a uniform magnetic field and it increases by increasing the angle of the cone in subcritical regime.

Keywords: Coulomb impurity, graphene cones, graphene quantum dots, topological defects.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2099

Authors: Irina E. Sukovataya, Oleg S. Sutormin, Valentina A. Kratasyuk

Abstract:

Effect of viscosity of media on kinetic parameters of the coupled enzyme system NADH:FMN-oxidoreductase–luciferase was investigated with addition of organic solvents (glycerol and sucrose), because bioluminescent enzyme systems based on bacterial luciferases offer a unique and general tool for analysis of the many analytes and enzymes in the environment, research and clinical laboratories and other fields. The possibility of stabilization and increase of activity of the coupled enzyme system NADH:FMN-oxidoreductase–luciferase activity in vicious aqueous-organic mixtures have been shown.

Keywords: The coupled enzyme system of bioluminescence bacteria NAD(P)H:FMN-oxidoreductase–luciferase, glycerol, stabilization of enzymes, sucrose.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1637

Authors: Snehasis Kundu, Koeli Ghoshal

Abstract:

In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6086

Authors: Atilla Akpinar

Abstract:

In this paper, we study on finite projective Hjelmslev planes M(Zq) coordinatized by Hjelmslev ring Zq (where prime power q = pk). We obtain finite hyperbolic Klingenberg planes from these planes under certain conditions. Also, we give a combinatorical result on M(Zq), related by deleting a line from lines in same neighbour.

Keywords: Finite Klingenberg plane, finite hyperbolic Klingenberg plane.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1146

Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1796

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

Abstract:

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

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1892

Authors: Liqiang Duan, Ma Jingkai, Lv Zhipeng, Haifan Cai

Abstract:

The integrated solar combined cycle (ISCC) system has a series of advantages such as increasing the system power generation, reducing the cost of solar power generation, less pollutant and CO₂ emission. In this paper, the parabolic trough collectors with direct steam generation (DSG) technology are considered to replace the heat load of heating surfaces in heat regenerator steam generation (HRSG) of a conventional natural gas combined cycle (NGCC) system containing a PG9351FA gas turbine and a triple pressure HRSG with reheat. The detailed model of the NGCC system is built in ASPEN PLUS software and the parabolic trough collectors with DSG technology is modeled in EBSILON software. ISCC-DSG systems with the replacement of single, two, three and four heating surfaces are studied in this paper. Results show that: (1) the ISCC-DSG systems with the replacement heat load of HPB, HPB+LPE, HPE2+HPB+HPS, HPE1+HPE2+ HPB+HPS are the best integration schemes when single, two, three and four stages of heating surfaces are partly replaced by the parabolic trough solar energy collectors with DSG technology. (2) Both the changes of feed water flow and the heat load of the heating surfaces in ISCC-DSG systems with the replacement of multi-stage heating surfaces are smaller than those in ISCC-DSG systems with the replacement of single heating surface. (3) ISCC-DSG systems with the replacement of HPB+LPE heating surfaces can increase the solar power output significantly. (4) The ISCC-DSG systems with the replacement of HPB heating surfaces has the highest solar-thermal-to-electricity efficiency (47.45%) and the solar radiation energy-to-electricity efficiency (30.37%), as well as the highest exergy efficiency of solar field (33.61%).

Keywords: HRSG, integration scheme, parabolic trough collectors with DSG technology, solar power generation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 892

Authors: Zilong Feng, Hong Li, Yang Liu, Siriguleng He

Abstract:

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.

Keywords: Pseudo-parabolic integro-differential equation, least squares mixed finite element method, adaptive method, a posteriori error estimates.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1318

Authors: A. F. Khadrawi

Abstract:

The transient hydrodynamics and thermal behaviors of fluid flow in open-ended vertical parallel-plate porous microchannel are investigated semi-analytically under the effect of the hyperbolic heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The Effects of Knudsen number , Darcy number , and thermal relaxation time  on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic heat conduction models. It is found that as  increases the slip in the hydrodynamic and thermal boundary condition increases. This slip in the hydrodynamic boundary condition increases as  increases. Also, the slip in the thermal boundary condition increases as  decreases especially the early stage of time.

Keywords: free convection, hyperbolic heat conduction, macroscopic heat conduction models in microchannel, porous media, vertical microchannel, microchannel thermal, hydrodynamic behavior.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1927

Authors: Mohammad Taghi Darvishi, Samad Kheybari

Abstract:

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.

Keywords: Parameter-expansion method, coupled van der pol oscillator, time-delay system.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1377

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

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

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1184