International Science Index

22
10011637
Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease
Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Paper Detail
239
downloads
21
10008260
A Study of General Attacks on Elliptic Curve Discrete Logarithm Problem over Prime Field and Binary Field
Abstract:
This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c
Paper Detail
839
downloads
20
10007600
An Evolutionary Algorithm for Optimal Fuel-Type Configurations in Car Lines
Abstract:
Although environmental concern is on the rise across Europe, current market data indicate that adoption rates of environmentally friendly vehicles remain extremely low. Against this background, the aim of this paper is to a) assess preferences of European consumers for clean-fuel cars and their characteristics and b) design car lines that optimize the combination of fuel types among models in the line-up. In this direction, the authors introduce a new evolutionary mechanism and implement it to stated-preference data derived from a large-scale choice-based conjoint experiment that measures consumer preferences for various factors affecting clean-fuel vehicle (CFV) adoption. The proposed two-step methodology provides interesting insights into how new and existing fuel-types can be combined in a car line that maximizes customer satisfaction.
Paper Detail
538
downloads
19
10006933
High Efficiency Perovskite Solar Cells Fabricated under Ambient Conditions with Mesoporous TiO2/In2O3 Scaffold
Abstract:

Mesoscopic perovskite solar cells (mp-PSCs) with mesoporous bilayer were fabricated under ambient conditions. The bilayer was formed by capping the mesoporous TiO2 layer with a layer of In2O3. CH3NH3I3-xClx mixed halide perovskite was prepared through the one-step method and was used as the light absorber. The mp-PSCs with the composite TiO2/In2O3 mesoporous layer exhibited optimized electrical parameters, compared with the PSCs that employed only a TiO2 mesoporous layer, with a current density of 23.86 mA/cm2, open circuit voltage of 0.863 V, fill factor of 0.6 and a power conversion efficiency of 11.2%. These results indicate that the formation of a proper semiconductor capping layer over the basic TiO2 mesoporous layer can facilitate the electron transfer, suppress the recombination and subsequently lead to higher charge collection efficiency.

Paper Detail
843
downloads
18
10005585
Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method
Authors:
Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Paper Detail
906
downloads
17
9997478
Is It Important to Measure the Volumetric Mass Density of Nanofluids?
Abstract:

The present study aims to measure the volumetric mass density of NiPd-heptane nanofluids synthesized using a one step method known as thermal decomposition of metal-surfactant complexes. The particle concentration is up to 7.55g/l and the temperature range of the experiment is from 20°C to 50°C. The measured values were compared with the mixture theory and good agreement between the theoretical equation and measurement were obtained. Moreover, the available nanofluids volumetric mass density data in the literature is reviewed.

Paper Detail
2335
downloads
16
17375
Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs
Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Paper Detail
1964
downloads
15
10001634
Prediction of Oxygen Transfer and Gas Hold-Up in Pneumatic Bioreactors Containing Viscous Newtonian Fluids
Abstract:

Pneumatic reactors have been widely employed in various sectors of the chemical industry, especially where are required high heat and mass transfer rates. This study aimed to obtain correlations that allow the prediction of gas hold-up (Ԑ) and volumetric oxygen transfer coefficient (kLa), and compare these values, for three models of pneumatic reactors on two scales utilizing Newtonian fluids. Values of kLa ​​were obtained using the dynamic pressure-step method, while e was used for a new proposed measure. Comparing the three models of reactors studied, it was observed that the mass transfer was superior to draft-tube airlift, reaching e of 0.173 and kLa of 0.00904s-1. All correlations showed good fit to the experimental data (R2≥94%), and comparisons with correlations from the literature demonstrate the need for further similar studies due to shortage of data available, mainly for airlift reactors and high viscosity fluids.

Paper Detail
1231
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14
10892
A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations
Authors:
Abstract:
In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.
Paper Detail
1221
downloads
13
1952
Plant Location Selection by Using a Three-Step Methodology: Delphi-AHP-VIKOR
Abstract:
Nowadays, the plant location selection has a critical impact on the performance of numerous companies. In this paper, a methodology is presented to solve this problem. The three decision making methods, namely Delphi, AHP and improved VIKOR, are hybridized in order to make the best use of information available based on the decision makers or experts. In this respect, the aim of using Delphi is to select the most influential criteria by a few decision makers. The AHP is utilized to give weights of the selected criteria. Finally, the improved VIKOR method is applied to rank alternatives. At the end of paper, an application example demonstrates the applicability of the proposed methodology.
Paper Detail
3627
downloads
12
15640
An Accurate Computation of Block Hybrid Method for Solving Stiff Ordinary Differential Equations
Authors:
Abstract:
In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.
Paper Detail
1214
downloads
11
3752
2 – Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations
Abstract:
In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.
Paper Detail
1681
downloads
10
1175
Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method
Abstract:

In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Paper Detail
6355
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9
2220
On One Application of Hybrid Methods For Solving Volterra Integral Equations
Abstract:
As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.
Paper Detail
1093
downloads
8
2925
Seven step Adams Type Block Method With Continuous Coefficient For Periodic Ordinary Differential Equation
Abstract:
We consider the development of an eight order Adam-s type method, with A-stability property discussed by expressing them as a one-step method in higher dimension. This makes it suitable for solving variety of initial-value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. Numerical results obtained using the proposed block form reveals that it is highly competitive with existing methods in the literature.
Paper Detail
1333
downloads
7
11056
An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations
Abstract:

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

Paper Detail
2763
downloads
6
11120
Research of a Multistep Method Applied to Numerical Solution of Volterra Integro-Differential Equation
Abstract:
Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.
Paper Detail
1172
downloads
5
4799
A New Physical Modeling for Multiquantum Well Structure APD Considering Nonuniformity of Electric Field in Active Regin
Abstract:
In the present work we model a Multiquantum Well structure Separate Absorption and Charge Multiplication Avalanche Photodiode (MQW-SACM-APD), while the Absorption region coincide with the MQW. We consider the nonuniformity of electric field using split-step method in active region. This model is based on the carrier rate equations in the different regions of the device. Using the model we obtain the photocurrent, and dark current. As an example, InGaAs/InP SACM-APD and MQW-SACM-APD are simulated. There is a good agreement between the simulation and experimental results.
Paper Detail
1208
downloads
4
2786
Statistical Analysis-Driven Risk Assessment of Criteria Air Pollutants: A Sulfur Dioxide Case Study
Authors:
Abstract:
A 7-step method (with 25 sub-steps) to assess risk of air pollutants is introduced. These steps are: pre-considerations, sampling, statistical analysis, exposure matrix and likelihood, doseresponse matrix and likelihood, total risk evaluation, and discussion of findings. All mentioned words and expressions are wellunderstood; however, almost all steps have been modified, improved, and coupled in such a way that a comprehensive method has been prepared. Accordingly, the SADRA (Statistical Analysis-Driven Risk Assessment) emphasizes extensive and ongoing application of analytical statistics in traditional risk assessment models. A Sulfur Dioxide case study validates the claim and provides a good illustration for this method.
Paper Detail
1372
downloads
3
6004
A New Derivative-Free Quasi-Secant Algorithm For Solving Non-Linear Equations
Abstract:
Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.
Paper Detail
1473
downloads
2
3785
Study on a Nested Cartesian Grid Method
Abstract:
In this paper, the local grid refinement is focused by using a nested grid technique. The Cartesian grid numerical method is developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. A finite volume method is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a nested grid solver are imposition of interface conditions on the inter-block and accurate discretization of the governing equation in cells that are with the inter-block as a control surface. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the spatial accuracy of the underlying solver. The present nested grid method has been tested by two numerical examples to examine its performance in the two dimensional problems. The numerical examples include flow past a circular cylinder symmetrically installed in a Channel and flow past two circular cylinders with different diameters. From the numerical experiments, the ability of the solver to simulate flows with complicated immersed boundaries is demonstrated and the nested grid approach can efficiently speed up the numerical solutions.
Paper Detail
1256
downloads
1
15171
A Force-directed Graph Drawing based on the Hierarchical Individual Timestep Method
Abstract:
In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.
Paper Detail
1587
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