A Nonlinear Explicit OneâStep Integration Scheme for ...
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A Nonlinear Explicit OneâStep Integration Scheme for ...
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A Nonlinear Explicit One‐Step Integration Scheme for Singular Autonomous Initial Value Problems Higinio Ramos Citation: AIP Conference Proceedings 936, 448 (2007); doi: 10.1063/1.2790175 View online: http://dx.doi.org/10.1063/1.2790175 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/936?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Approximate solution for fourth order linear fuzzy initial value problem AIP Conf. Proc. 1482, 302 (2012); 10.1063/1.4757484 Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point AIP Conf. Proc. 1389, 241 (2011); 10.1063/1.3636712 Exponentially Fitted Explicit Hybrid Method For Solving Special Second Order Initial Value Problems AIP Conf. Proc. 1309, 467 (2010); 10.1063/1.3525148 Computation of Consistent Initial Values for Nonlinear Index 3 DAEs AIP Conf. Proc. 936, 607 (2007); 10.1063/1.2790220 Generalized Dirichlet to Neumann map for moving initial-boundary value problems J. Math. Phys. 48, 013502 (2007); 10.1063/1.2405405
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A Nonlinear Explicit One-Step Integration Scheme for Singular Autonomous Initial Value Problems Higinio Ramos 1 Escuela Politecnica Superior de Zamora. Grupo de Computation Cientifica. Universidad de Salamanca. Salamanca. Spain. Abstract. Recently the author has presented a non-standard algorithm of second-order for numerically solving initial-value problems [1]. This algorithm performs well for different kinds of problems such as singular or singularly perturbed problems. Now, in this paper an improved method of third order is proposed for solving autonomous problems of special type. To test the efficiency of the new method a well-known numerical example is provided. Keywords: non-linear method, initial-value problems, singular initial-value problems, singularly perturbed initial-value problems, stiff problems, blow-up ODE problems PACS: 02.30.Hq, 02.60.Lj
INTRODUCTION An autonomous scalar initial-value problem (IVP) given by
y' = f(y), y,f(y)&R,
y(a)=yo, xe[a,b]cR,
will be considered, which is assumed to have a unique solution that may have singularities. The conventional explicit one-step method for (1) can be written as y„ + i = ay„ + h
