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Discretizations of nonlinear differential equations using explicit finite order methods

✍ Scribed by Benito Chen; Francisco Solis

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
608 KB
Volume
90
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this work we study the appearance of spurious solutions when first-order differential equations with unimodal righthand sides are discretized using Runge-Kutta schemes. These spurious solutions are explained in terms of the iteration functions. Schemes that produce good approximating solutions for much longer times are given. (~) 1998 Elsevier Science B.V. All rights reserved.

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We construct explicit single step discretizations of linear, non-homogeneous initial boundary value problems. These methods use polynomial approximations for the time discretization. The order reduction phenomenon, present when a fully discrete Runge-Kutta is used, is avoided and the maximum expecte