1,721,006 research outputs found
On the construction of a new generalization of Runge-Kutta methods
No full textWe give an overview of the construction of algebraic conditions for determining the order of Runge-Kutta methods and describe a novel extension for numerically solving systems of differential equations. The new schemes, called Elementary Differential Runge-Kutta methods, include as a subset Runge-Kutta methods, Taylor series methods, Multiderivative Runge-Kutta methods. We outline how order conditions have been constructed for the new schemes using B-series and their composition and give details relating to a Mathematica implementation. © 2003 Published by Elsevier Science B. V
Increment formulations for rounding error reduction in the numerical solution of structured differential systems
No full textStrategies for reducing the effect of cumulative rounding errors in geometric numerical integration are outlined. The focus is, in particular, on the solution of separable Hamiltonian systems using explicit symplectic integration methods and on solving orthogonal matrix differential systems using projection. Examples are given that demonstrate the advantages of an increment formulation over the standard implementation of conventional integrators. We describe how the aforementioned special purpose integration methods have been set up in a uniform, modular and extensible framework being developed in the problem solving environment Mathematica. © 2002 Elsevier Science B.V. All rights reserved
An image reconstruction algorithm in tomography: A version for the CRAY X-MP vector computer
No full textThe present paper summarizes the main features of an algorithm for image reconstruction from radiographic projections. Starting from an analysis of the "filtered back-projection algorithm," a new routine is built which performs "filtering" of the projections through a particular filter-function. The results are then tested by means of the simulation of a tomographic problem (C.T.) implemented on the CRAY X-MP/48 vector processor. © 1989
Solving orthogonal matrix differential systems in Mathematica
No full textA component of a new environment for the numerical solution of ordinary differential equations in Mathematica is outlined. We briefly describe how special purpose integration methods can be constructed to solve structured dynamical systems. In particular we focus on the solution of orthogonal matrix differential systems using projection. Examples are given to illustrate the advantages of a projection scheme over conventional integration methods. © Springer-Verlag 2002
Symplectic methods for separable Hamiltonian systems
No full textThis paper focuses on the solution of separable Hamiltonian systems using explicit symplectic integration methods. Strategies for reducing the effect of cumulative rounding errors are outlined and advantages over a standard formulation are demonstrated. Procedures for automatically choosing appropriate methods are also described. © Springer-Verlag 2002
The parallel recursive decoupling algorithm for solving tridiagonal linear systems
No full textIn this paper we describe a new tridiagonal equation solver, based on a rank-one updating strategy and the repeated partitioning of the system matrix into 2 × 2 submatrices. On this basis, a recursive decoupling method is developed [2,3], which operates on the tridiagonal linear system, enabling the solution to be expressed in explicit form and solved independently on a multiprocessor system. We will show, in fact, that the Recursive Decoupling method is intrinsically parallel and can be implemented as an efficient parallel algorithm. © 1993
Computer generation of numerical methods for ordinary differential equations
No full textWe describe some issues related to the derivation of numerical methods for ordinary differential equations. We discuss how to establish algebraic constraints on the free parameters of the methods which control the quality of the numerical solution. Furthermore, we describe a Mathematica package which essentially automates the derivation process for Runge-Kutta methods. The package incorporates many new facilities to aid in analysis and construction and we will give examples to plain the design and motivation for the functionality. We also discuss some techniques that are useful for obtaining solutions to the algebraic constraints
Block partitioning in the parallel recursive decoupling method
No full textNew 3 × 3 and 4 × 4 block partitioning techniques are presented for the Recursive Decoupling Method and tested on a set of tridiagonal linear systems. A comparison with the original 2 × 2 partitioning method [1], for accuracy, numerical stability and parallel performance, is also considered. All tests have been carried out on parallel shared memory architecture, such as the Sequent Balance 8000 multiprocessor and the CRAY Y-MP parallel/vector supercomputer. © 1994, Taylor & Francis Group, LLC. All rights reserved
Some LP algorithms using orthogonal matrices
No full textThe aim of this paper is the exploitation of the properties of orthogonal matrices in the development of a new theoretical approach and in the implementation of iterative routines for solving linear programming problems. © 1996, Instituto di Elaborazione della Informazione del CNR. All rights reserved
Modeling and Simulation of a miRNA Regulatory Network of the PTEN Gene
Full text linkThe PTEN onco-suppressor gene is likely to play an important role in the onset of brain cancer, namely glioblastoma multiforme. Consequently, the PTEN regulatory network, involving microRNAs and competitive endogenous RNAs, becomes a crucial tool for understanding the mechanism related to low levels of expression in cancer patients. This paper introduces a novel model for the regulation of PTEN whose solution is approximated by a high-dimensional system of ordinary differential equations under the assumption that the Law of Mass Action applies. Extensive numerical simulations are presented that mirror parts of the biological subtext that lies behind various alterations. Given the complexity of processes involved in the acquisition of empirical data, initial conditions and reaction rates were inferred from the literature. Despite this, the proposed model is shown to be capable of capturing biologically reasonable behaviors of inter-species interactions, thus representing a positive result, which encourages pursuing the possibility of experimenting on data hopefully provided by omics disciplines
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