scholarly journals Accuracy Evaluation of Classical Integer Order Based and Direct Non-integer Order Numerical Algorithms of Non-integer Order Derivatives and Integrals Computations

2014 ◽  
Author(s):  
Dariusz W. Brzeziński ◽  
Piotr Ostalczyk
Keyword(s):  
Numerical Algorithms ◽  
Accuracy Evaluation ◽  
Integer Order

scholarly journals Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus

2018 ◽  
Vol 3 (2) ◽  
pp. 487-502 ◽  
Author(s):  
Dariusz W. Brzeziński
Keyword(s):  
Fourier Series ◽  
Fractional Calculus ◽  
Accuracy Assessment ◽  
Numerical Algorithms ◽  
Convergence Acceleration ◽  
General Purpose ◽  
Inverse Laplace Transform ◽  
Fourier Series Expansion ◽  
Accuracy Evaluation ◽  
Computational Accuracy

AbstractIn the paper we present results of accuracy evaluation of numerous numerical algorithms for the numerical approximation of the Inverse Laplace Transform. The selected algorithms represent diverse lines of approach to this problem and include methods by Stehfest, Abate and Whitt, Vlach and Singhai, De Hoog, Talbot, Zakian and a one in which the FFT is applied for the Fourier series convergence acceleration. We use C++ and Python languages with arbitrary precision mathematical libraries to address some crucial issues of numerical implementation. The test set includes Laplace transforms considered as difficult to compute as well as some others commonly applied in fractional calculus. Evaluation results enable to conclude that the Talbot method which involves deformed Bromwich contour integration, the De Hoog and the Abate and Whitt methods using Fourier series expansion with accelerated convergence can be assumed as general purpose high-accuracy algorithms. They can be applied to a wide variety of inversion problems.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Accuracy Evaluation of Power Grid Reduction Method Utilizing Differential Evolution under the Condition of Increasing Renewables Deployment

2019 ◽  
Vol 139 (1) ◽  
pp. 27-38
Author(s):  
Takahiro Shimoo ◽  
Misao Kimura ◽  
Yuji Ishihara ◽  
Takafumi Maeda
Keyword(s):  
Differential Evolution ◽  
Reduction Method ◽  
Power Grid ◽  
Accuracy Evaluation

Delivery of Low Basal Rates in Different Insulin Pumps—An Accuracy Evaluation

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 972-P
Author(s):  
RALPH ZIEGLER ◽  
ULRIKE KAMECKE ◽  
DELIA WALDENMAIER ◽  
CORNELIA HAUG ◽  
GUIDO FRECKMANN
Keyword(s):  
Accuracy Evaluation ◽  
Insulin Pumps

Numerical Algorithms and Software for Spectral Factorization Problems

1988 ◽  
Author(s):  
Matt Wette ◽  
Alan J. Laub
Keyword(s):  
Numerical Algorithms ◽  
Spectral Factorization

Preface to the special issue, CMAM 2011, no. 3.

2011 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Ivan Gavrilyuk ◽  
Boris Khoromskij ◽  
Eugene Tyrtyshnikov
Keyword(s):  
Separation Of Variables ◽  
Numerical Algorithms ◽  
Multilevel Methods ◽  
High Dimensional ◽  
Special Issue ◽  
High Dimensions ◽  
Guiding Principle ◽  
Tensor Methods ◽  
Closed World ◽  
The One

Abstract In the recent years, multidimensional numerical simulations with tensor-structured data formats have been recognized as the basic concept for breaking the "curse of dimensionality". Modern applications of tensor methods include the challenging high-dimensional problems of material sciences, bio-science, stochastic modeling, signal processing, machine learning, and data mining, financial mathematics, etc. The guiding principle of the tensor methods is an approximation of multivariate functions and operators with some separation of variables to keep the computational process in a low parametric tensor-structured manifold. Tensors structures had been wildly used as models of data and discussed in the contexts of differential geometry, mechanics, algebraic geometry, data analysis etc. before tensor methods recently have penetrated into numerical computations. On the one hand, the existing tensor representation formats remained to be of a limited use in many high-dimensional problems because of lack of sufficiently reliable and fast software. On the other hand, for moderate dimensional problems (e.g. in "ab-initio" quantum chemistry) as well as for selected model problems of very high dimensions, the application of traditional canonical and Tucker formats in combination with the ideas of multilevel methods has led to the new efficient algorithms. The recent progress in tensor numerical methods is achieved with new representation formats now known as "tensor-train representations" and "hierarchical Tucker representations". Note that the formats themselves could have been picked up earlier in the literature on the modeling of quantum systems. Until 2009 they lived in a closed world of those quantum theory publications and never trespassed the territory of numerical analysis. The tremendous progress during the very recent years shows the new tensor tools in various applications and in the development of these tools and study of their approximation and algebraic properties. This special issue treats tensors as a base for efficient numerical algorithms in various modern applications and with special emphases on the new representation formats.

Numerical Algorithms & Parallel Tasking.

1985 ◽  
Author(s):  
Virginia Kelma
Keyword(s):  
Numerical Algorithms
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