Plasma dispersion function is an important parameter in the ionospheric physics, fast and accurate computation of this function is extremely valuable in practical use. Many numerical algorithms have been proposed, and...
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Plasma dispersion function is an important parameter in the ionospheric physics, fast and accurate computation of this function is extremely valuable in practical use. Many numerical algorithms have been proposed, and it is very necessary to evaluate their performances. In present paper, we first introduce an alternative method to derive the plasma dispersion function and its first derivative using the differential and integral calculus method, and then compare the accuracy and efficiency of three well-known numerical algorithms (algorithm of Steven G. Johnson, algorithm 916, and algorithm of Abrarov and Quine) in Matlab environment under the uniform and non-uniform distribution of the grid-points, and finally analyze the variations of the real and imaginary part of the plasma dispersion function and its first derivative preliminarily. The results show that Abrarov and Quine's algorithm performs better than other two numerical algorithms from the comprehensive viewpoint of accuracy and efficiency. (C) 2019 Elsevier Ltd. All rights reserved.
An antenna array composed of one transmitter and multi-receivers and dedicated to measuring terminal trajectory of the target of interest, which is supposed to be in uniform rectilinear motion, is set up. On the basis...
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ISBN:
(纸本)9783540741701
An antenna array composed of one transmitter and multi-receivers and dedicated to measuring terminal trajectory of the target of interest, which is supposed to be in uniform rectilinear motion, is set up. On the basis of the model, the Vector parameter that can uniquely determine the terminal trajectory of target is introduced, and the measurement equations which describe the respective relationships between the Vector parameter and the instantaneous Doppler frequency and the phase differences extracted from echoes are established. Taking advantage of the measurement equations, we propose an algorithm of estimating the Vector parameter without resolving the phase difference ambiguity;furthermore, the detailed steps in estimating the Vector parameter using numerical optimization techniques are put forward. The Monte Carlo simulation results demonstrate the effectiveness and reliability of our numerical algorithm compared with the traditional method.
There are many numerical algorithms for solving the fractional-order differential equations (FODEs). The numerical algorithms are very different, and it is difficult to compare their performances. To solve this proble...
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ISBN:
(纸本)9781509046577
There are many numerical algorithms for solving the fractional-order differential equations (FODEs). The numerical algorithms are very different, and it is difficult to compare their performances. To solve this problem, some different FODEs with the known analytical solution are designed and proposed, they could be used as the benchmark problems for testing the numerical algorithms. A Simulink block diagram scheme is proposed for solving these benchmark problems, and the computing errors and the running times are reported. These benchmark problems and the solutions are constituted as a framework, and the numerical algorithms for solving the FODEs could be compared in the same framework. The comparing result could assess which algorithm is better to a concrete FODE.
Almost four decades passed after the discovery of solitons and infinite dimensional integrable systems. The theory of integrable systems has had great impact to wide area in physics and mathematics. In this paper an a...
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ISBN:
(纸本)0769521509
Almost four decades passed after the discovery of solitons and infinite dimensional integrable systems. The theory of integrable systems has had great impact to wide area in physics and mathematics. In this paper an approach to numerical algorithms in terms of integrable systems is surveyed. Some integrable systems of Lax form describe continuous flows of efficient numerical algorithms, for example, the QR algorithm and the Jacobi algorithm. Discretizations of integrable systems in tau-function level enable us to formulate algorithms for computing continued fractions such as the qd algorithm and the discrete Schur flow. A new singular value decomposition (I-SVD) algorithm is designed by using a discrete integrable system defined by the Christoffel-Darboux identity for orthogonal polynomials.
algorithms for computing the inverse Laplace transform that consist essentially in choosing a series expansion for the original function are particularly effective in many cases and are widely used. The main purpose o...
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algorithms for computing the inverse Laplace transform that consist essentially in choosing a series expansion for the original function are particularly effective in many cases and are widely used. The main purpose of this paper is to review these algorithms in the context of regularization. We relate this viewpoint to the design of reliable algorithms destined to be run on finite precision arithmetic systems.
Fragmentation of the often used numerical algorithms for inclusion into the library of parallel numerical subroutines are considered. algorithms and programs fragmentation allow to create parallel programs that can be...
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ISBN:
(纸本)9783642032745
Fragmentation of the often used numerical algorithms for inclusion into the library of parallel numerical subroutines are considered. algorithms and programs fragmentation allow to create parallel programs that can be executed on parallel computers of different types (multiprocessors and/or multicomputers) and can be dynamically tuned to all the available resources. Programs' fragmentation is the way of automatic providing of the dynamic properties of parallel programs, like dynamic load balancing. algorithm's fragmentation is a technological method of numerical algorithms parallelization which provides their effective parallel implementation.
Image inpainting is a technique that utilizes information from surrounding areas to restore damaged or missing parts. To achieve binary image inpainting with mathematical tools and numerical techniques, an effective m...
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Image inpainting is a technique that utilizes information from surrounding areas to restore damaged or missing parts. To achieve binary image inpainting with mathematical tools and numerical techniques, an effective mathematical model and an efficient, stable numerical solver are essential. This work aims to propose a practical and unconditionally stable numerical algorithm for image inpainting. A penalized Allen-Cahn equation is derived from a free energy using a variational approach. The proposed mathematical model achieves inpainting by eliminating the damaged region with the constraint of surrounding image values. The operator splitting strategy is used to split the original model into two subproblems. The first one is the classical Allen-Cahn equation, and the second one is a penalization equation. For the Allen-Cahn equation, a linear and strong stability-preserving factorization scheme is adopted to calculate the intermediate solution. Then, the final solution is explicitly updated from a simple correction step. The governing equation is discretized in space using the finite difference method. We analytically prove that the proposed algorithm is unconditionally stable and uniquely solvable. In the numerical simulations, we first verify the efficiency and stability via several simple benchmarks. The capability of binary image inpainting is validated by comparing the present and previous results. By slightly adjusting the governing equation, the proposed method can work well in achieving image inpainting of various gray-valued images. Finally, the proposed method is extended into three-dimensional space to show its effectiveness in restoring damaged 3D objects. The main scientific contributions are: (i) an efficient and practical numerical method is developed for image inpainting;(ii) the unconditional stability and unique solvability have been analytically estimated;(iii) extensive numerical experiments are implemented to validate the stability and capability
Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for *** chemical dissolution-front ins...
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Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for *** chemical dissolution-front instability problem in fluid-saturated porous rocks is no *** this kind of instability problem has both the conventional(***)and the unconventional(***)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous *** this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this *** the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic *** particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous *** related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.
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