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1 – 10 of 239Averaging methods with closure approximations and perturbative methods have been discussed in control literature. Suggests that continuing mathematical developments in the…
Abstract
Averaging methods with closure approximations and perturbative methods have been discussed in control literature. Suggests that continuing mathematical developments in the decomposition method allow a better approach without the disadvantages of the above.
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G. Adomian, R.C. Rach and R.E. Meyers
The decomposition model has demon‐strated accurate and physically realistic solutions of systems modelled by non‐linear equations. Linear or determin‐istic equations become simple…
Abstract
The decomposition model has demon‐strated accurate and physically realistic solutions of systems modelled by non‐linear equations. Linear or determin‐istic equations become simple special cases and the result is a general method of solution connecting the fields of ordinary and partial differential equations. No linearisation or resort to numerically intensive discretised methods is involved. The avoidance of these limiting and restrictive methods offers physically correct solutions as well as insights into the behaviour of real systems where non‐linear effects play a crucial role. In difficult applications, such as those now approached by computational fluid dynamics, the potential saving in computation will be substantial. The method clearly offers the potential of a significant step forward in the rapid solution of complex applications in a time and memory‐saving manner with important implications for computa‐tional analysis and modelling.
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Masao Shimada, David Tae, Tao Xue, Rohit Deokar and K K Tamma
The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a…
Abstract
Purpose
The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces.
Design/methodology/approach
In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics.
Findings
Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability.
Originality/value
The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation.
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Jean-Pierre Fouque and Xianwen Zhou
Gaussian copula is by far the most popular copula used in the financial industry in default dependency modeling. However, it has a major drawback – it does not exhibit tail…
Abstract
Gaussian copula is by far the most popular copula used in the financial industry in default dependency modeling. However, it has a major drawback – it does not exhibit tail dependence, a very important property for copula. The essence of tail dependence is the interdependence when extreme events occur, say, defaults of corporate bonds. In this paper, we show that some tail dependence can be restored by introducing stochastic volatility on a Gaussian copula. Using perturbation methods we then derive an approximate copula – called perturbed Gaussian copula in this paper.
Presents one possible synthesis of the artificial neural network using linking algebra. The mathematical model given is the basis for such a neural network organization. The…
Abstract
Presents one possible synthesis of the artificial neural network using linking algebra. The mathematical model given is the basis for such a neural network organization. The problem which appears is a mode of realization of the artificial neuron. Starting with the experience gained by many experiments, the model of a neuron that can be realized in the memory of computer is presented.
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R. SERFATY and R.M. COTTA
A hybrid numerical‐analytical approach, based on recent developments in the generalized integral transform technique, is presented for the solution of a class of non‐linear…
Abstract
A hybrid numerical‐analytical approach, based on recent developments in the generalized integral transform technique, is presented for the solution of a class of non‐linear transient convection‐diffusion problems. The original partial differential equation is integral transformed into a denumerable system of coupled non‐linear ordinary differential equations, which is numerically solved for the transformed potentials. The hybrid analysis convergence is illustrated by considering the one‐dimensional non‐linear Burgers equation and numerical results are presented for increasing truncation orders of the infinite ODE system.
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Théophile Mavoungou and Yves Cherruault
The study of the convergence of Adomian's method presents some difficulties when applied to real problems. Proposes a convergence proof of this technique adapted to non‐linear…
Abstract
The study of the convergence of Adomian's method presents some difficulties when applied to real problems. Proposes a convergence proof of this technique adapted to non‐linear partial differential equations. Solves some real examples numerically.
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Difference schemes for hyperbolic systems of conservation laws occasionally converge to an unphysical weak solution, i.e. a weak solution containing discontinuities for which the…
Abstract
Difference schemes for hyperbolic systems of conservation laws occasionally converge to an unphysical weak solution, i.e. a weak solution containing discontinuities for which the entropy condition is violated. These unphysical discontinuities, when they exist as solutions of the difference scheme, tend to exhibit a surprising stability under perturbations. We point out here that this can be explained by an energy inequality, which is valid for the discrete approximation but which is not valid as applied to the differential equation itself. In spite of this difficulty, many simple difference schemes are highly successful at converging to the physically correct weak solution. A mechanism for this is given; we show that for shocks of moderate strength, there are numerous quadratic forms in the dependent variables which can serve effectively as entropy functions, i.e. for which an inequality exists determining the physically correct weak solution. It is shown how the limits of the solutions of a difference scheme will often necessarily satisfy such an inequality; as they are generally weak solutions of the given system, they must thus be the correct weak solutions.
Qiang Li, Jiahuan Du, Xugang Zhang, Chuanli Qin, Zheng Jin and Xuduo Bai
The purpose of this paper is to develop porous nitrogen-enriched carbon (NC-U) with high nitrogen concentration and high specific capacitance (Cpe) as the electrode material for…
Abstract
Purpose
The purpose of this paper is to develop porous nitrogen-enriched carbon (NC-U) with high nitrogen concentration and high specific capacitance (Cpe) as the electrode material for supercapacitors.
Design/methodology/approach
NC-U was obtained by carbonization of polyvinylpyrrolidone/melamine formaldehyde resin (PVP/MF) with different contents of urea. In comparison, NC-K was also prepared by the KOH activation method. A series of asymmetric supercapacitors with NC as a negative electrode was assembled. The composition, microstructure and electrochemical properties of NC and their supercapacitors were studied.
Findings
The results show that NC-U shows irregular particles with a porous honeycomb structure. High Cpe was obtained for urea-treated NC-U because of the improvement of nitrogen, conductivity and specific surface area (S BET ). NC-U50 with 13.15 per cent at nitrogen has the highest Cpe of 148.53 F/g because of the highest concentration of N-6 and N-5. NC-K with higher S BET has lower Cpe than NC-U50 because of its lower nitrogen concentration. When the specific power of the supercapacitor with NC-U50 as a negative electrode is 1,565.56 W/kg, its specific energy is still 4.35 Wh/kg. There is only 5.9 per cent decay in Cpe over 1,000 cycles.
Research limitations/implications
NC-U is a suitable electrode material for supercapacitors, which can be used in the field of electric vehicles to solve the problems of energy shortage and environmental pollutions.
Originality/value
Porous NC-U based on PVP/MF/urea composites with high nitrogen concentration and Cpe is novel, and it owns good electrochemical properties.
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