scholarly journals A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Yueyue Pan ◽  
Lifei Wu ◽  
Xiaozhong Yang
Keyword(s):  
Stability And Convergence ◽  
Fisher Equation ◽  
Spatial Accuracy ◽  
New Class ◽  
Intrinsic Parallelism ◽  
Parallel Difference ◽  
Difference Methods ◽  
Explicit And Implicit Schemes ◽  
The Difference ◽  
Time Accuracy

This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit-implicit (PASE-I) and pure alternating segment implicit-explicit (PASI-E) are constructed by taking simple classical explicit and implicit schemes, combined with the alternating segment technique. The existence, uniqueness, linear absolute stability, and convergence for the solutions of PASE-I and PASI-E schemes are well illustrated. Both theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are linearly absolute stable, with 2-order time accuracy and 2-order spatial accuracy. Compared with the implicit scheme and the Crank–Nicolson (C-N) scheme, the computational efficiency of the PASE-I (PASI-E) scheme is greatly improved. The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the Burgers–Fisher equation.

scholarly journals An Efficient Parallel Approximate Algorithm for Solving Time Fractional Reaction-Diffusion Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xiaozhong Yang ◽  
Lifei Wu
Keyword(s):  
Reaction Diffusion ◽  
Implicit Scheme ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Approximate Algorithm ◽  
Diffusion Equations ◽  
Intrinsic Parallelism ◽  
The Difference ◽  
Time Accuracy ◽  
Fractional Reaction

In this paper, we construct pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) difference algorithms for time fractional reaction-diffusion equations (FRDEs). They are a kind of difference schemes with intrinsic parallelism and based on classical explicit scheme and classical implicit scheme combined with alternating segment technology. The existence and uniqueness analysis of solutions of the parallel difference schemes are given. Both the theoretical proof and the numerical experiment show that PASE-I and PASI-E schemes are unconditionally stable and convergent with second-order spatial accuracy and 2−α order time accuracy. Compared with implicit scheme and E-I (I-E) scheme, the computational efficiency of PASE-I and PASI-E schemes is greatly improved. PASE-I and PASI-E schemes have obvious parallel computing properties, which shows that the difference schemes with intrinsic parallelism in this paper are feasible to solve the time FRDEs.

Anti-adhesion Molecules in IBD: Does Gut Selectivity Really Make the Difference?

2019 ◽  
Vol 25 (1) ◽  
pp. 19-24 ◽  
Author(s):  
Ferdinando D'Amico ◽  
Giulia Roda ◽  
Laurent Peyrin-Biroulet ◽  
Silvio Danese
Keyword(s):  
Adhesion Molecules ◽  
Biological Treatment ◽  
Current Data ◽  
New Drugs ◽  
Inflammatory Infiltration ◽  
New Class ◽  
Bowel Diseases ◽  
Inflammatory Bowel ◽  
The Difference ◽  
Necrosis Factor

Inflammatory Bowel Disease is lifetime chronic progressive inflammatory disease. A considerable portion of patients, do not respond or lose response or experience side effect to “traditional” biological treatment such as anti-tumor necrosis factor (TNF)-α agents. The concept that the blockade of T cell traffic to the gut controls inflammation has stimulated the development of new drugs which selectively targets molecules involved in controlling cell homing to the intestine. The result is the reduction of the chronic inflammatory infiltration in the gut. In this regard, anti-adhesion molecules represent a new class of drugs for patients who don’t respond or lose response to traditional therapy. Moreover, some of these molecules such as vedolizumab, offer the advantage to target the delivery of a drug to the gut (gut selectivity) which could increase clinical efficacy and limit potential adverse events. In this article, we will give an overview of the current data on anti-adhesion molecules in Inflammatory Bowel Diseases.

DEVELOPMENT OF A MODEL FOR DECISION SUPPORT SYSTEMS FOR MANAGING THE PROCESS OF INVESTING IN CYBERSECURITY TAKING INTO ACCOUNT MULTIFACTORIALITY

2021 ◽  
Vol 75 (3) ◽  
pp. 70-75
Author(s):  
B.E. Yagaliyeva ◽  
◽  
B.B. Akhmetov ◽  
V.A. Lakhno ◽  
G.S. Zhilkishbayeva ◽  
...  
Keyword(s):  
Information Technologies ◽  
Complex Structure ◽  
Multidimensional Space ◽  
Simulation Environment ◽  
Matlab Simulation ◽  
Program Code ◽  
New Class ◽  
Multistage Games ◽  
The Difference ◽  
Investment Process

A model for managing the investment process is proposed, based on the example of investing in cybersecurity of national scale informatization objects, taking into account the multifactorial nature of this process. The difference between this model and those previously developed is that, firstly, it considers the investment process as a complex structure, for which it is not enough to model it as a one-factor category. Second, our model is based on the solution of a bilinear multi-step quality game with several terminal surfaces. The solution is obtained within the framework of the scheme of a new class of bilinear multistage games describing the interaction of objects in a multidimensional space. Consideration of the investment process in such a setting makes it possible to adequately describe the process of searching for rational strategies of players in the course of investing in information technologies. The study made it possible to implement the program code of the model in the MatLab simulation environment.

I. On a new class of bodies homologous to hydrocyanic acid. -I

1868 ◽  
Vol 16 ◽  
pp. 144-147
Keyword(s):  
Acetic Acid ◽  
Formic Acid ◽  
Hydrocyanic Acid ◽  
Methyl Group ◽  
New Class ◽  
Atom Group ◽  
The Difference

The typical transformation which hydrocyanic acid undergoes when sub­mitted, under appropriate circumstances, to the action of water, is capable of assuming two different forms when accomplished in its homologues. If the hydrocyanic molecule be found to fix the elements of two mole­cules of water, yielding ultimately formic acid and ammonia, it is obvious that the atom group which in the homologues of hydrocyanic acid we as­sume in the place of hydrogen may be eliminated when these homologues are decomposed by water in conjunction either with formic acid or with ammonia. To take an example: —When acting with water upon the sim­plest homologue of hydrocyanic acid (upon cyanide of methyl), we may ex­pect to see the methyl-group separating either in the form of methyl-formic, i. e . acetic acid, or in the form of methyl-ammonia, i. e . of methylamine, The difference of the two reactions and their relation to the metamorphosis of hydrocyanic acid itself are exhibited by the following equations:

Propagator Method for Numerical Solution of Convective Fisher Equation

2011 ◽  
Vol 222 ◽  
pp. 387-390
Author(s):  
Daiga Zaime ◽  
Janis S. Rimshans ◽  
Sharif E. Guseynov
Keyword(s):  
Difference Scheme ◽  
Iteration Process ◽  
Fisher Equation ◽  
Implicit Difference Scheme ◽  
Nonlinear Convection ◽  
First Order ◽  
Truncation Errors ◽  
Propagator Method ◽  
Left And Right ◽  
The Difference

Propagator numerical method was developed as an effective tool for modeling of linear advective dispersive reactive (ADR) processes [1]. In this work implicit propagator difference scheme for Fisher equation with nonlinear convection (convective Fisher equation) is elaborated. Our difference scheme has truncation errors of the second order in space and of the first order in time. Iteration process for implicit difference scheme is proposed by introducing forcing terms in the left and right sides of the difference equation. Convergence and stability criterions for the elaborated implicit propagator difference scheme are obtained.

scholarly journals Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment

2020 ◽  
Vol 25 (12) ◽  
pp. 2178-2198
Author(s):  
Lucjan Sapa ◽  
Bogusław Bożek ◽  
Katarzyna Tkacz–Śmiech ◽  
Marek Zajusz ◽  
Marek Danielewski
Keyword(s):  
Finite Difference Methods ◽  
Mass Conservation ◽  
Three Dimensions ◽  
Uniqueness Of Solutions ◽  
Strongly Coupled ◽  
Nonlinear Parabolic ◽  
Implicit Difference Schemes ◽  
Coupled Boundary Conditions ◽  
Difference Methods ◽  
The Difference

Over the last two decades, there have been tremendous advances in the computation of diffusion and today many key properties of materials can be accurately predicted by modelling and simulations. In this paper, we present, for the first time, comprehensive studies of interdiffusion in three dimensions, a model, simulations and experiment. The model follows from the local mass conservation with Vegard’s rule and is combined with Darken’s bi-velocity method. The approach is expressed using the nonlinear parabolic–elliptic system of strongly coupled differential equations with initial and nonlinear coupled boundary conditions. Implicit finite difference methods, preserving Vegard’s rule, are generated by some linearization and splitting ideas, in one- and two-dimensional cases. The theorems on the existence and uniqueness of solutions of the implicit difference schemes and the consistency of the difference methods are studied. The numerical results are compared with experimental data for a ternary Fe-Co-Ni system. A good agreement of both sets is revealed, which confirms the strength of the method.

scholarly journals A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaozhong Yang ◽  
Xu Dang
Keyword(s):  
Parallel Computing ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Parallel Difference ◽  
Fractional Reaction ◽  
Crank Nicolson

Abstract The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference schemes. The class of parallel difference schemes constructed in this paper, based on the classical Crank–Nicolson (C–N) scheme and classical explicit and implicit schemes, combines with alternating segment techniques. We illustrate the unique existence, unconditional stability, and convergence of the parallel difference scheme solution theoretically. Numerical experiments verify the theoretical analysis, which shows that the IASC–N scheme has second order spatial accuracy and $2-\alpha $ 2 − α order temporal accuracy, and the computational efficiency is greatly improved compared with the implicit scheme and C–N scheme. The IASC–N scheme has ideal computation accuracy and obvious parallel computing properties, showing that the IASC–N parallel difference method is effective for solving time fractional reaction–diffusion equation.

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