The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Neurohr Christian - One of the best experts on this subject based on the ideXlab platform.
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Computing period matrices and the Abel-Jacobi map of superelliptic curves
American Mathematical Society, 2019Co-Authors: Molin Pascal, Neurohr ChristianAbstract:International audienceWe present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation y m = f (x). It relies on rigorous numerical integration of differentials between Weierstrass points, which is done using Gauss Method if the curve is hyperelliptic (m = 2) or the Double-Exponential Method. The algorithm is implemented and makes it possible to reach thousands of digits accuracy even on large genus curves
Galina Ya. Benderskaya - One of the best experts on this subject based on the ideXlab platform.
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International Conference on Computational Science (2) - On Implementation of Vector Gauss Method for Solving Large-Scale Systems of Index 1 Differential-Algebraic Equations
Lecture Notes in Computer Science, 2002Co-Authors: Gennady Y. Kulikov, Galina Ya. BenderskayaAbstract:In the paper we further develop the idea of parallel factorization of nonzero blocks of sparse coefficient matrices of the linear systems arising from discretization of large-scale index 1 differential-algebraic problems by Runge-Kutta Methods and their following solving by Newton-type iterations. We formulate a number of theorems that give estimates for the local fill-in of such matrices on some stages of Gaussian elimination. As the result, we derive that only the suggested modification of Gauss Method appeared to be effiective and economical one from the standpoint of CPU time and RAM.
R. Vigneswaran - One of the best experts on this subject based on the ideXlab platform.
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A NON-LINEAR SCHEME BASED ON PROJECTION Method FOR TWO STAGE Gauss Method
International journal of pure and applied mathematics, 2015Co-Authors: R. VigneswaranAbstract:A variety of linear iteration schemes with reduced linear algebra costs have been proposed to solve the non-linear equations arising in the im- plementation of implicit Runge-Kutta Methods as an alternative to the mod- ified Newton iteration scheme. In this paper, a non-linear scheme based on projection Method is proposed to accelerate the convergence rates of linear it- eration schemes. In particular, for an s-stage Runge-Kutta Method, an s-step non-linear scheme is proposed, which is computationally more efficient. For two stage Gauss Method, some theoretical results are established in order to improve the rate of convergence of linear iteration schemes. Finally, some nu- merical experiments are carried out to confirm the results established in this
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Some Efficient Schemes with Improving Rate of Convergence for Two-stage Gauss Method
2014Co-Authors: R. VigneswaranAbstract:Various iteration schemes have been proposed to solve the non-linear equations arising in the implementation of implicit Runge-Kutta Methods. A modified Newton scheme is typically used to solve these equations. As an alternative to this scheme, iteration schemes, which sacrifice super-linear convergence for reduced linear algebra costs, have been proposed. A scheme of this type proposed in [11] avoids expensive vector transformations and is computationally more efficient. The rate of convergence of this scheme is examined in [11] when it is applied to the scalar test differential equation
Juan I. Montijano - One of the best experts on this subject based on the ideXlab platform.
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Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta Methods of the Gauss type
Journal of Computational and Applied Mathematics, 2009Co-Authors: Manuel Calvo, Juan I. Montijano, J. M. Franco, Luis RándezAbstract:The construction of exponentially fitted Runge-Kutta (EFRK) Methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. Based on the symplecticness, symmetry, and exponential fitting properties, two new three-stage RK integrators of the Gauss type with fixed or variable nodes, are obtained. The new exponentially fitted RK Gauss type Methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(@lt),exp([email protected])}, @[email protected]?C, and in particular {sin(@wt),cos(@wt)} when @[email protected], @[email protected]?R. The algebraic order of the new integrators is also analyzed, obtaining that they are of sixth-order like the classical three-stage RK Gauss Method. Some numerical experiments show that the new Methods are more efficient than the symplectic RK Gauss Methods (either standard or else exponentially fitted) proposed in the scientific literature.
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A Code Based on Gauss Methods for Second Order Differential Systems
AIP Conference Proceedings, 2007Co-Authors: S. González-pinto, Juan I. Montijano, Luis Rández, S. Pérez-rodríguez, R. Rojas-belloAbstract:A code for the numerical solution of Initial Value Problems for Second Order Systems y″(t) = f(t,y), is presented. The code, of general scope, can cope satisfactorily with oscillatory problems specially when the low frequencies are dominant and low to medium accuracy is required. It is of interest for medium to large dimensional problems, specially when banded or circulant Jacobian matrices arise in the discretization in space via MoL of some time‐dependant partial differential equations, such as vibrating bars. The code is equipped with a reliable global error estimate and it is based on the two‐stage Runge‐Kutta Gauss Method. The stage values are solved by an special Newton‐type iteration and the predictors were carefully chosen to minimize the number of iterations per integration step. A guess for the initial step‐size is provided and a variable step‐size policy is used. A continuously differentiable solution based on the Hermite interpolation is supplied. The performance of the code on some interestin...
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Iterative schemes for Gauss Methods
Computers & Mathematics with Applications, 1994Co-Authors: S. González-pinto, Concepción González-concepción, Juan I. MontijanoAbstract:Abstract In this paper, we consider a class of iterative schemes for implicit Runge-Kutta Methods and we study the convergence of these schemes for a family of nonlinear stiff problems. A particular convergent scheme for the two stage Gauss Method is proposed and the order and linear stability properties are analyzed. Finally, some numerical experiments are included in order to show the efficiency of the Method.
Molin Pascal - One of the best experts on this subject based on the ideXlab platform.
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Computing period matrices and the Abel-Jacobi map of superelliptic curves
American Mathematical Society, 2019Co-Authors: Molin Pascal, Neurohr ChristianAbstract:International audienceWe present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation y m = f (x). It relies on rigorous numerical integration of differentials between Weierstrass points, which is done using Gauss Method if the curve is hyperelliptic (m = 2) or the Double-Exponential Method. The algorithm is implemented and makes it possible to reach thousands of digits accuracy even on large genus curves