An adaptive stepsize algorithm for the numerical solving of initial-value problems

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica

Militaru Romulus¹ 

[1] Department of Applied Mathematics, University of Craiova, 13 A.I. Cuza, 200589 Craiova, Romania.;

关键词: initial value problems;    adaptive numerical methods;    local truncation error approach;    one-step numerical methods;    numerical computation;    primary 65l05, 65l70, 65l12;   

DOI  :  10.1515/auom-2015-0012

来源: DOAJ

【 摘 要 】

The present paper focuses on the efficient numerical solving of initial-value problems (IVPs) using digital computers and one-step numerical methods. We start from considering that the integration stepsize is the crucial factor in determining the number of calculations required and the amount of work involved to obtain the approximate values of the exact solution of a certain problem for a given set of points, within a prescribed computational accuracy, is proportional to the number of accomplished iterations. We perform an analysis of the local truncation error and we derive an adaptive stepsize algorithm which coupled with a certain one-step numerical method makes the use of this structure more computationally effective and insures that the estimated values of the exact solution are in agreement with an imposed accuracy. We conclude with numerical computations proving the efficiency of the proposed step selection algorithm.

【 授权许可】

Unknown