Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique. (14th February 2013)

• Record Type: Journal Article
• Authors: Duan, Jun‐Sheng; Rach, Randolph; Lin, Shi‐Ming
• Is Part Of: Mathematical methods in the applied sciences. Volume 36:Number 13(2013:Sep. 15)
• Page Start: 1790
• Page End: 1804
• Publication Date: 2013-02-14
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2725
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2725-abs-0001"> <title>Abstract</title> <p id="mma2725-para-0001">We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>