Search results

1 – 10 of 13
To view the access options for this content please click here
Article

Ping He and Yangmin Li

The purpose of this paper is to investigate the analytical solution of a hyperbolic partial differential equation (PDE) and its application.

Abstract

Purpose

The purpose of this paper is to investigate the analytical solution of a hyperbolic partial differential equation (PDE) and its application.

Design/methodology/approach

The change of variables and the method of successive approximations are introduced. The Volterra transformation and boundary control scheme are adopted in the analysis of the reaction-diffusion system.

Findings

A detailed and complete calculation process of the analytical solution of hyperbolic PDE (1)-(3) is given. Based on the Volterra transformation, a reaction-diffusion system is controlled by boundary control.

Originality/value

The introduced approach is interesting for the solution of hyperbolic PDE and boundary control of the reaction-diffusion system.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 10 no. 2
Type: Research Article
ISSN: 1756-378X

Keywords

To view the access options for this content please click here
Article

Omar Abu Arqub

The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and…

Abstract

Purpose

The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.

Design/methodology/approach

Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed.

Findings

The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations.

Originality/value

In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article

Maria T. Ibáñez and H. Power

The main objective is to develop an efficient BEM scheme for the numerical solution of two‐dimensional heat problems. Our scheme will be of the re‐initialization type, in…

Abstract

The main objective is to develop an efficient BEM scheme for the numerical solution of two‐dimensional heat problems. Our scheme will be of the re‐initialization type, in which the domain integrals are computed by a recursion relation which depends only on the boundary temperature and flux at previous time step. To obtain the re‐initialization approach, we will use in the integral representation formula a Green function corresponding to zero temperature in a box containing the original domain, instead of using the classical free space fundamental solution. This Green function is given in terms of the original fundamental solution plus a regular solution of the heat equation inside the domain under consideration. It can therefore be used in the integral representation formula of the heat equation (direct formulation) to obtain the solution of a heat problem in such a domain. The Green function mentioned can be obtained by the images method, and the resulting source series can also be rewritten in terms of a double Fourier series, that we will use in the domain integral of the integral representation formula to transform such integral into equivalent surface integrals.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 10 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article

Utku Erdogan, Murat Sari and Huseyin Kocak

The purpose of this study is to propose a non-classical method to obtain efficient and accurate numerical solutions of the advection–diffusion–reaction equations.

Abstract

Purpose

The purpose of this study is to propose a non-classical method to obtain efficient and accurate numerical solutions of the advection–diffusion–reaction equations.

Design/methodology/approach

Unlike conventional numerical methods, this study proposes a numerical scheme using outer Newton iteration applied to a time-dependent PDE. The linearized time dependent PDE is discretized by trapezoidal rule, which is second order in time, and by spline-based finite difference method of fourth order in space.

Findings

Using the proposed technique, even when relatively large time step sizes are used in computations, the efficiency of the proposed procedure is very clear for the numerical examples in comparison with the existing classical methods.

Originality/value

This study, unlike these classical methods, proposes an alternative approach based on linearizing the nonlinear problem at first, and then discretizing it by an appropriate scheme. This technique helps to avoid considering the convergence issues of Newton iteration applied to nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. The linearized PDE can be solved by implicit time integrator, which enables the use of large time step size.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here

Abstract

Details

Understanding Financial Risk Management, Second Edition
Type: Book
ISBN: 978-1-78973-794-3

To view the access options for this content please click here
Article

Jaroslav Mackerle

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix…

Abstract

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

Details

Engineering Computations, vol. 13 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

To view the access options for this content please click here
Article

Farshid Mossaiby and Mehdi Ghaderian

The purpose of this paper is to extend the meshless local exponential basis functions (MLEBF) method to the case of nonlinear and linear, variable coefficient partial…

Abstract

Purpose

The purpose of this paper is to extend the meshless local exponential basis functions (MLEBF) method to the case of nonlinear and linear, variable coefficient partial differential equations (PDEs).

Design/methodology/approach

The original version of MLEBF method is limited to linear, constant coefficient PDEs. The reason is that exponential bases which satisfy the homogeneous operator can only be determined for this class of problems. To extend this method to the general case of linear PDEs, the variable coefficients along with all involved derivatives are first expanded. This expanded form is evaluated at the center of each cloud, and is assumed to be constant over the entire cloud. The solution procedure is followed as in the former version. Nonlinear problems are first converted to a succession of linear, variable coefficient PDEs using the Newton-Kantorovich scheme and are subsequently solved using the aforementioned approach until convergence is achieved.

Findings

The results obtained show good performance of the method as solution to a wide range of problems. The results are compared with the well-known methods in the literature such as the finite element method, high-order finite difference method or variants of the boundary element method.

Originality/value

The MLEBF method is a simple yet effective tool for analyzing various kinds of problems. It is easy to implement with high parallelization potential. The proposed method addresses the biggest limitation of the method, and extends it to linear, variable coefficient PDEs as well as nonlinear ones.

To view the access options for this content please click here
Article

Xiaojing Zheng, Xusong Xu and Cui Cui Luo

The purpose of this paper is to improve the behaviors coordination mechanism, to maintain the system's long time‐scale and stable competitive capability, when the agents…

Abstract

Purpose

The purpose of this paper is to improve the behaviors coordination mechanism, to maintain the system's long time‐scale and stable competitive capability, when the agents in the system focus on cooperating with each other.

Design/methodology/approach

Effort level for every agent, whose dynamics can be described as a stochastic partial differential equation, and the incentive of effort as the control of the corresponding agent, are introduced to describe agents' behavior abstracted. The cooperative stochastic differential game model is constructed: first, the optimal resolve trajectory mapping with profit maximization of the system are obtained, then the transitory imputation coupled with effort initial state of the system by introducing dynamic Shapley value imputation method. Based on the results obtained, the profit distribution strategies and the equilibration incentive compensation mechanism are given, due to the evolution law of the payoff and the state variable.

Findings

It is concluded that: the transitory compensation to agent for efforts and incentive, which can be changed with the system state at current and in history and in future changed, would guarantee the realization of the Shapley value imputation throughout the game horizon.

Originality/value

In this paper, the interactivity between agents in the system is considered first. The dynamical Shapley imputation mechanism and the transitory compensatory mechanism are provided to make the imputation more stable and feasible.

To view the access options for this content please click here
Article

Fausto A.A. Barbuto and Renato Machado Cotta

Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect…

Abstract

Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect to the co‐ordinate system chosen to represent the geometry under consideration. A quite general formulation of a two‐dimensional steady‐state diffusion problem is initially considered, and a formal solution is provided. The original partial differential equation is analytically transformed into an infinite system of ordinary differential equations for the transformed velocity field in the flow direction. On truncation to a sufficiently large finite order, adaptively chosen to meet prescribed accuracy requirements, well‐established numerical schemes for boundary value problems are utilized, readily available in scientific subroutines libraries. Illustrates convergence rates for a few typical duct geometries and critically examines previously reported numerical solutions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article

Arman Shojaei, Mirco Zaccariotto and Ugo Galvanetto

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF…

Abstract

Purpose

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.

Design/methodology/approach

The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.

Findings

The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.

Originality/value

The current study paves the road for future studies on dynamic and static crack propagation problems.

Details

Engineering Computations, vol. 34 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

1 – 10 of 13