TITLE

ANALYTIC ITERATIVE PROCESSES AND NUMERICAL ALGORITHMS FOR STIFF PROBLEMS

AUTHOR(S)
Faleichik, B. V.
PUB. DATE
April 2008
SOURCE
Computational Methods in Applied Mathematics;2008, Vol. 8 Issue 2, p116
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The goal of the research is to construct practicable numerical algorithms for stiff systems of ordinary differential equations which let you increase the accuracy of the approximate solution without decreasing the length of the time interval. To achieve this goal, we have constructed a family of new iterative analytic processes generalising the Picard process. For a basic representative of this family, we demonstrate its better convergence properties on a scalar linear problem in comparison with the classical Picard process. For the general form of such iterative processes, we discuss their connection with existing methods for operator equations and propose a method for choosing their parameters. The efficiency of this parameter determination method is justified with a numerical experiment. In conclusion we propose a general approach to the construction of numerical algorithms which is based on the discretisation of the constructed iterative analytic processes.
ACCESSION #
33967223

 

Related Articles

  • Gauss-Seidel method for multi-valued inclusions with Z mappings. Allevi, E.; Gnudi, A.; Konnov, I.; Schaible, S. // Journal of Global Optimization;May2012, Vol. 53 Issue 1, p97 

    We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under...

  • Parareal and Spectral Deferred Corrections. Minion, Michael L.; Williams, Sarah A. // AIP Conference Proceedings;9/15/2008, Vol. 1048 Issue 1, p388 

    A new class of iterative time parallel methods for initial value ordinary differential equations are developed. Methods based on a parallel variation of spectral deferred corrections (SDC) are compared and contrasted with the parareal method. It is shown that there is a strong similarity between...

  • Superlinear/Quadratic One-step Smoothing Newton Method forP0-NCP. Li Ping Zhang; Ji Ye Han; Zheng Hai Huang // Acta Mathematica Sinica;Feb2005, Vol. 21 Issue 1, p117 

    We propose a one-step smoothing Newton method for solving the non-linear complementarity problem withP0-function (P0-NCP) based on the smoothing symmetric perturbed Fisher function (for short, denoted as the SSPF-function). The proposed algorithm has to solve only one linear system of equations...

  • Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers. Meziane, Belkacem; A├»ssani, Ahmed // International Journal of Optics;2008, p1 

    A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These...

  • Two-grid algorithms for linear and nonlinear elliptic problems based on HSS iteration method. Shishun Li; Zhengda Huang // Journal of Computational Analysis & Applications;Jan2012, Vol. 14 Issue 1, p880 

    In this paper, based on the idea of Hermitian/skew-Hermitian splitting(HSS) iteration method, we present several two-grid (two level) algorithms for solving a large class of linear and nonlinear second-order elliptic boundary value problems. These algorithms reduce the nonsymmetric linear system...

  • Combined Selection of Tile Sizes and Unroll Factors Using Iterative Compilation. Knijnenburg, P. M. W.; Kisuki, T.; O'Boyle, M. F. P. // Journal of Supercomputing;Jan2003, Vol. 24 Issue 1, p43 

    Loop tiling and unrolling are two important program transformations to exploit locality and expose instruction level parallelism, respectively. However, these transformations are not independent and each can adversely affect the goal of the other. Furthermore, the best combination will vary...

  • Feasibility in uncapacitated networks: The effect of individual arcs and nodes. Ghannadan, Saied; Wallace, Stein W. // Annals of Operations Research;1996, Vol. 64 Issue 1-4, p197 

    The purpose of this paper is to investigate the effect of individual arcs and nodes on the description of feasibility in an uncapacitated network. This is done by developing an iterative algorithm for finding all (necessary) Gale--Hoffman inequalities for the network.

  • THE SEMILOCAL CONVERGENCE OF THE HALLEY'S METHOD.  // Annals of the University Dunarea de Jos of Galati: Fascicle II, ;2011, Vol. 34 Issue 1, p113 

    The article presents a study of Halley's method, which is among the most well-known one-iteration methods. Halley's method is a third order root-finding algorithm in numerical analysis used for functions of one real variable with a continuous second derivative. A numerical example is presented...

  • One improvement of the law of the iterated logarithm for the maximum scheme. Akbash, K.; Matsak, I. // Ukrainian Mathematical Journal;Jan2013, Vol. 64 Issue 8, p1290 

    The greatest lower bound is found in the law of the iterated logarithm for the maximum scheme.

Share

Other Topics