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1 – 10 of 183
Article
Publication date: 17 September 2008

Joan C. Micó, Antonio Caselles and Pantaleón D. Romero

The purpose is to present a new formal approach based on a partial integrodifferential equation, the space‐time state transition equation (STSTE), and on a set of general…

Abstract

Purpose

The purpose is to present a new formal approach based on a partial integrodifferential equation, the space‐time state transition equation (STSTE), and on a set of general equations with which space‐time dynamical models of complex systems, such as social systems and ecosystems, can be built.

Design/methodology/approach

The STSTE provides the partial derivative of the density of a state‐variable with regard to time as a sum of time rates and space‐time rates. Time rates describe the dynamics of the system for each space‐point irrespectively of the other points, whilst space‐time rates describe this evolution as a consequence of the relation of each space‐point with a given set of other points of the space. This relation contains integrals over the accessibility domains (sets of space‐points with which each space‐point is related).

Findings

The STSTE is provided for any system of space‐coordinates and is compared with the reaction‐diffusion models (RD). The reason why it is more convenient to work with the STSTE than with the RD to model complex systems in the context of social systems and ecosystems is indicated.

Practical implications

An urban system (the city of Valencia, Spain) is presented as an application; an analytical solution strategy is stated under the simplest hypothesis for computing space‐time rates, and a computer program for the situation is developed to obtain numerical solutions.

Originality/value

A numerical comparison between the new STSTE model and the RD shows that, the STSTE model produces better results than the reaction diffusion model in validation.

Details

Kybernetes, vol. 37 no. 7
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 3 August 2020

Yaser Rostami

This paper aims to present a new method for the approximate solution of two-dimensional nonlinear Volterra–Fredholm partial integro-differential equations with boundary conditions…

Abstract

Purpose

This paper aims to present a new method for the approximate solution of two-dimensional nonlinear Volterra–Fredholm partial integro-differential equations with boundary conditions using two-dimensional Chebyshev wavelets.

Design/methodology/approach

For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of Chebyshev wavelets. The use of these operational matrices simplifies considerably the structure of the computation used for a set of the algebraic system has been obtained by using the collocation points and solved.

Findings

Theorem for convergence analysis and some illustrative examples of using the presented method to show the validity, efficiency, high accuracy and applicability of the proposed technique. Some figures are plotted to demonstrate the error analysis of the proposed scheme.

Originality/value

This paper uses operational matrices of two-dimensional Chebyshev wavelets and helps to obtain high accuracy of the method.

Details

Engineering Computations, vol. 38 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 29 July 2020

Joan Carles Mico, Salvador Amigó, Antonio Caselles and Pantaleón D. Romero

The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the…

Abstract

Purpose

The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the biological levels of description.

Design/methodology/approach

The relationship between the two mentioned levels of description is provided by two mathematical models as follows: the response model and the bridge model. The response model (an integro-differential equation) is capable to reproduce the personality dynamics as a consequence of a determined stimulus. The invariance principle asserts that the response model can reproduce personality dynamics at the two levels of description. The bridge model (a second-order partial differential equation) can be deduced as a consequence of this principle: it provides the co-evolution of the general factor of personality (GFP) (mind), the it is an immediate early gene (c-fos) and D3 dopamine receptor gene (DRD3) gens and the glutamate neurotransmitter (body).

Findings

An application case is presented by setting up two experimental designs: a previous pilot AB pseudo-experimental design (AB) pseudo-experimental design with one subject and a subsequent ABC experimental design (ABC) experimental design with another subject. The stimulus used is the stimulant drug methylphenidate. The response and bridge models are validated with the outcomes of these experiments.

Originality/value

The mathematical approach here presented is based on a holistic personality model developed in the past few years: the unique trait personality theory, which claims for a single personality trait to understand the overall human personality: the GFP.

Book part
Publication date: 1 December 2008

Jingyi Zhu

The credit migration process contains important information about the dynamics of a firm's credit quality, therefore, it has a significant impact on its relevant credit…

Abstract

The credit migration process contains important information about the dynamics of a firm's credit quality, therefore, it has a significant impact on its relevant credit derivatives. We present a jump diffusion approach to model the credit rating transitions which leads to a partial integro-differential equation (PIDE) formulation, with defaults and rating changes characterized by barrier crossings. Efficient and reliable numerical solutions are developed for the variable coefficient equation that result in good agreement with historical and market data, across all credit ratings. A simple adjustment in the credit index drift converts the model to be used in the risk-neutral setting, which makes it a valuable tool in credit derivative pricing.

Details

Econometrics and Risk Management
Type: Book
ISBN: 978-1-84855-196-1

Article
Publication date: 1 January 2013

Ning Rong and Farzad Alavi Fard

The purpose of this paper is to propose a model for ruin‐contingent life annuity (RCLA) contracts under a jump diffusion model, where the dynamics of volatility is governed by the…

Abstract

Purpose

The purpose of this paper is to propose a model for ruin‐contingent life annuity (RCLA) contracts under a jump diffusion model, where the dynamics of volatility is governed by the Heston stochastic volatility framework. The paper aims to illustrate that the proposed jump diffusion process, for both asset price and stochastic volatility, will provide a more realistic pricing model for RCLA contracts in comparison to existing models.

Design/methodology/approach

Under the assumption of the deterministic withdrawals, the authors use a partial integro differential equation (PIDE) approach to develop the pricing scheme for the fair value of the lump sum charges of RCLA contracts. Consequently, the authors employ an elegant numerical scheme, finite difference method, for solving the PIDEs for the reference portfolio, as well as the volatility. The findings show that a different pricing behaviour of the RCLA contracts under the authors' model parameters is obtained compared to that in the existing literature.

Findings

RCLA pricing in the complete market often underestimates the jump risk and the persistent factor in the volatility process. The authors' generalized model shows how these two random sources of risks can be precisely characterized.

Research limitations/implications

The parameter values used in the numerical analysis require more empirical evidence. Hence, in order for more precise pricing practice, the calibration from real data is needed.

Practical implications

The model, as adopted in this study, for pricing of RCLA contracts should provide a general guideline for the commercialization of this product by insurance companies.

Social implications

The demand for RCLA contracts as an alternative to the commonly‐practised annuitization option has recently increased, rapidly, among the soon‐to‐retire baby boomers. This paper investigates the fair value of this particular product, which could be beneficial to researchers for a better understanding of the product design.

Originality/value

This is the first research paper which prices the RCLA contracts in the incomplete market. The gap between RCLA contract pricing and studies of jump diffusion models for derivative pricing, in the literature, is therefore filled.

Article
Publication date: 21 June 2019

Mohsen Hadadian Nejad Yousefi, Seyed Hossein Ghoreishi Najafabadi and Emran Tohidi

The purpose of this paper is to develop an efficient and reliable spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations.

Abstract

Purpose

The purpose of this paper is to develop an efficient and reliable spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations.

Design/methodology/approach

In this study, the considered two-dimensional unsteady advection-diffusion equations are transformed into the equivalent partial integro-differential equations via integrating from the considered unsteady advection-diffusion equation. After this stage, by using Chebyshev polynomials of the first kind and the operational matrix of integration, the integral equation would be transformed into the system of linear algebraic equations. Robustness and efficiency of the proposed method were illustrated by six numerical simulations experimentally. The numerical results confirm that the method is efficient, highly accurate, fast and stable for solving two-dimensional unsteady advection-diffusion equations.

Findings

The proposed method can solve the equations with discontinuity near the boundaries, the advection-dominated equations and the equations in irregular domains. One of the numerical test problems designed specially to evaluate the performance of the proposed method for discontinuity near boundaries.

Originality/value

This study extends the intention of one dimensional Chebyshev approximate approaches (Yuksel and Sezer, 2013; Yuksel et al., 2015) for two-dimensional unsteady advection-diffusion problems and the basic intention of our suggested method is quite different from the approaches for hyperbolic problems (Bulbul and Sezer, 2011).

Article
Publication date: 10 October 2020

Soraya Torkaman, Ghasem Barid Loghmani, Mohammad Heydari and Abdul-Majid Wazwaz

The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel…

Abstract

Purpose

The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method.

Design/methodology/approach

The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs.

Findings

Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method.

Originality/value

The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 23 November 2018

Neeraj Dhiman and Mohammad Tamsir

The purpose of this paper is to present a new method, namely, “Re-modified quintic B-spline collocation method” to solve the Kuramoto–Sivashinsky (KS) type equations. In this…

Abstract

Purpose

The purpose of this paper is to present a new method, namely, “Re-modified quintic B-spline collocation method” to solve the Kuramoto–Sivashinsky (KS) type equations. In this method, re-modified quintic B-spline functions and the Crank–Nicolson formulation is used for space and time integration, respectively. Five examples are considered to test out the efficiency and accuracy of the method. The main objective is to develop a method which gives more accurate results and reduces the computational cost so that the authors require less memory storage.

Design/methodology/approach

A new collocation technique is developed to solve the KS type equations. In this technique, quintic B-spline basis functions are re-modified and used to integrate the space derivatives while time derivative is discretized by using Crank–Nicolson formulation. The discretization yields systems of linear equations, which are solved by using Gauss elimination method with partial pivoting.

Findings

Five examples are considered to test out the efficiency and accuracy of the method. Finally, the present study summarizes the following outcomes: first, the computational cost of the proposed method is the less than quintic B-spline collocation method. Second, the present method produces better results than those obtained by Lattice Boltzmann method (Lai and Ma, 2009), quintic B-spline collocation method (Mittal and Arora, 2010), quintic B-spline differential quadrature method (DQM) (Mittal and Dahiya, 2017), extended modified cubic B-spline DQM (Tamsir et al., 2016) and modified cubic B-splines collocation method (Mittal and Jain, 2012).

Originality/value

The method presented in this paper is new to best of the authors’ knowledge. This work is the original work of authors and the manuscript is not submitted anywhere else for publication.

Details

Multidiscipline Modeling in Materials and Structures, vol. 18 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 14 March 2019

Vinicius Piro Barragam, Andre Fenili and Ijar Milagre da Fonseca

The purpose of this paper is the dynamic analysis of the coupled rotation and vibration motion of a system containing a central rigid body to which is attached a flexible beam.

Abstract

Purpose

The purpose of this paper is the dynamic analysis of the coupled rotation and vibration motion of a system containing a central rigid body to which is attached a flexible beam.

Design/methodology/approach

The methodology includes the Lagrange’s formulation by using the extended Hamilton’s Principle in conjunction with the assumed modes method to describe the system of equations by ordinary differential equations. The first unconstrained mode of vibration was considered as the solution for the transversal displacement. Such mode emerges as the eigenvalue problem solution associated to the dynamics of the system. The control strategy adopted is a nonlinear analogy of the linear quadratic regulator problem as the Riccati equation is solved at every integration step during the numerical solutions. This strategy is known as state-dependent Riccati equation.

Findings

By means of computational simulations, it was found the relation between controlled motion and inertia ratio.

Research limitations/implications

This work is limited to planar case and fixed hub.

Practical implications

Practical implications of this work realize the design of lighter yet dexterous structures.

Originality/value

The contribution of this paper is the position and vibration control of a flexible beam accounting for nonlinearity effects and the fact that the structure to where it is clamped has a comparable inertia.

Details

Aircraft Engineering and Aerospace Technology, vol. 91 no. 7
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 10 August 2010

I˙nan Ates¸ and Ahmet Yıldırım

The purpose of this paper is to consider the time‐fractional diffusion‐wave equation. The time‐fractional diffusion equation is obtained from the standard diffusion equation by…

Abstract

Purpose

The purpose of this paper is to consider the time‐fractional diffusion‐wave equation. The time‐fractional diffusion equation is obtained from the standard diffusion equation by replacing the first‐order time derivative with a fractional derivative of order α ∈ (0, 2]. The fractional derivatives are described in the Caputo sense.

Design/methodology/approach

The two methods in applied mathematics can be used as alternative methods for obtaining an analytic and approximate solution for different types of differential equations.

Findings

Four examples are presented to show the application of the present techniques. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity.

Originality/value

In this paper, the variational iteration and homotopy perturbation methods are used to obtain a solution of a fractional diffusion equation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 183