Performance assessment of exponential Rosenbrock method for large systems of ODE

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Acute compensatory eating following exercise is associated with implicit hedonic wanting for food

The efficacy of exercise to promote weight loss could potentially be undermined by its influence on explicit or implicit processes of liking and wanting for food which in turn alter food preference. The present study was designed to examine hedonic and homeostatic mechanisms involved in the acute effects of exercise on food intake. 24 healthy female subjects were recruited to take part in two counterbalanced activity sessions; 50 min of high intensity (70% max heart rate) exercise (Ex) or no exercise (NEx). Subjective appetite sensations, explicit and implicit hedonic processes, food preference and energy intake (EI) were measured immediately before and after each activity session and an ad libitum test meal. Two groups of subjects were identified in which exercise exerted different effects on compensatory EI and food preference. After exercise, compensators (C) increased their EI, rated the food to be more palatable, and demonstrated increased implicit wanting. Compensators also showed a preference for high-fat sweet food compared with non-compensators (NC), independent of the exercise intervention. Exercise-induced changes in the hedonic response to food could be an important consideration in the efficacy of using exercise as a means to lose weight. An enhanced implicit wanting for food after exercise may help to explain why some people overcompensate during acute eating episodes. Some individuals could be resistant to the beneficial effects of exercise due to a predisposition to compensate for exercise-induced energy expenditure as a result of implicit changes in food preferences.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Implicit discount rates and fisheries management : is there a relationship?

Fishers are faced with multiple risks, including unpredictability of future catch rates, prices and costs. While the latter are largely beyond the control of fisheries managers, effective fisheries management should reduce uncertainty about future catches. Different management instruments are likely to have different impacts on the risk perception of fishers, and this should manifest itself in their implicit discount rate. Assuming licence and quota values represent the net present value of the flow of expected future profits, then a proxy for the implicit discount rate of vessels in a fishery can be derived by the ratio of the average level of profits to the average licence/quota value. From this, an indication of the risk perception can be derived, assuming higher discount rates reflect higher levels of systematic risk. In this paper, we apply the capital asset pricing model (CAPM) to determine the risk premium implicit in the discount rates for a range of Australian fisheries, and compare this with the set of management instruments in place. We test the assumption that rights based management instruments lower perceptions of risk in fisheries. We find little evidence to support this assumption. although the analysis was based on only limited data.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Negative mood, implicit alcohol-related memory, and alcohol use in young adults: The moderating effect of alcohol expectancy

Objective Alcohol-related implicit (preconscious) cognitive processes are established and unique predictors of alcohol use, but most research in this area has focused on alcohol-related implicit cognition and anxiety. This study extends this work into the area of depressed mood by testing a cognitive model that combines traditional explicit (conscious and considered) beliefs, implicit alcohol-related memory associations (AMAs), and self-reported drinking behavior. Method Using a sample of 106 university students, depressed mood was manipulated using a musical mood induction procedure immediately prior to completion of implicit then explicit alcohol-related cognition measures. A bootstrapped two-group (weak/strong expectancies of negative affect and tension reduction) structural equation model was used to examine how mood changes and alcohol-related memory associations varied across groups. Results Expectancies of negative affect moderated the association of depressed mood and AMAs, but there was no such association for tension reduction expectancy. Conclusion Subtle mood changes may unconsciously trigger alcohol-related memories in vulnerable individuals. Results have implications for addressing subtle fluctuations in depressed mood among young adults at risk of alcohol problems.

Improving matching process in social network using implicit and explicit user information

Personalised social matching systems can be seen as recommender systems that recommend people to others in the social networks. However, with the rapid growth of users in social networks and the information that a social matching system requires about the users, recommender system techniques have become insufficiently adept at matching users in social networks. This paper presents a hybrid social matching system that takes advantage of both collaborative and content-based concepts of recommendation. The clustering technique is used to reduce the number of users that the matching system needs to consider and to overcome other problems from which social matching systems suffer, such as cold start problem due to the absence of implicit information about a new user. The proposed system has been evaluated on a dataset obtained from an online dating website. Empirical analysis shows that accuracy of the matching process is increased, using both user information (explicit data) and user behavior (implicit data).