Search results for "Step method"
showing 10 items of 10 documents
Diffusion stabilizes cavity solitons in bidirectional lasers
2009
We study the influence of field diffusion on the spatial localized structures (cavity solitons) recently predicted in bidirectional lasers. We find twofold positive role of the diffusion: 1) it increases the stability range of the individual (isolated) solitons; 2) it reduces the long-range interaction between the cavity solitons. Latter allows the independent manipulation (writing and erasing) of individual cavity solitons.
NUMERICAL ALGORITHMS
2013
For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a …
Sub-critical filtration conditions of commercial hollow-fibre membranes in a submerged anaerobic MBR (HF-SAnMBR) system: The effect of gas sparging i…
2012
A submerged anaerobic MBR demonstration plant with two commercial hollow-fibre ultrafiltration systems (PURON®, Koch Membrane Systems, PUR-PSH31) was operated using municipal wastewater at high levels of mixed liquor total solids (MLTS) (above 22gL -1). A modified flux-step method was applied to assess the critical flux (J C) at different gas sparging intensities. The results showed a linear dependency between J C and the specific gas demand per unit of membrane area (SGD m). J C ranged from 12 to 19LMH at SGD m values of between 0.17 and 0.5Nm 3h -1m -2, which are quite low in comparison to aerobic MBR. Long-term trials showed that the membranes operated steadily at fluxes close to the est…
Robust and Efficient IMEX Schemes for Option Pricing under Jump-Diffusion Models
2013
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump diffusion process. The schemes include the families of IMEX-midpoint, IMEXCNAB and IMEX-BDF2 schemes. Each family is defined by a convex parameter c ∈ [0, 1], which divides the zeroth-order term due to the jumps between the implicit and explicit part in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint fa…
Generalized differential transform method for nonlinear boundary value problem of fractional order
2015
Abstract In this paper the generalized differential transform method is applied to obtain an approximate solution of linear and nonlinear differential equation of fractional order with boundary conditions. Several numerical examples are considered and comparisons with the existing solution techniques are reported. Results show that the method is effective, easier to implement and very accurate when applied for the solution of fractional boundary values problems.
Real lattices modelled by the nonlinear Schrödinger equation and its generalizations
2006
We present the analysis of two dimerized lattices : a bi-inductance electrical network with macroscopic wave modes, an antiferromagnetic chain whith microscopic spin waves. Using the multiple scale technique of reductive perturbation we show that the original discrete equations of motion can be reduced to a Nonlinear Schrodinger equation with complex coefficients for the first system and two coupled Nonlinear Schrodinger equations for the second system. The possible solutions of these equations are discussed in relation with our numerical simulations and real experiments.
On a step method and a propagation of discontinuity
2019
In this paper we analyze how to compute discontinuous solutions for functional differential equations, looking at an approach which allows to study simultaneously continuous and discontinuous solutions. We focus our attention on the integral representation of solutions and we justify the applicability of such an approach. In particular, we improve the step method in such a way to solve a problem of vanishing discontinuity points. Our solutions are considered as regulated functions.
Some efficient algorithms for the solution of a single nonlinear equation
1981
High order methods for the numerical solution of nonlinear scalar equations are proposed which are more efficient than known procedures, and a unified approach to various methods suggested in literature is given.
A Marching in Space and Time (MAST) solver of the shallow water equations. Part I: The 1D model
2007
A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of Partial Differential Equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to …
IMEX schemes for pricing options under jump–diffusion models
2014
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump-diffusion process. The schemes include the families of IMEX-midpoint, IMEX-CNAB and IMEX-BDF2 schemes. Each family is defined by a convex combination parameter [email protected]?[0,1], which divides the zeroth-order term due to the jumps between the implicit and explicit parts in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restric…