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Nyström methods and singular second-order differential equations

✍ Scribed by David Benko; Daniel C. Biles; Mark P. Robinson; John S. Spraker

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
276 KB
Volume
56
Category
Article
ISSN
0898-1221

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✦ Synopsis

Chawla, Jain and Subramanian studied the application of Nyström methods to a class of singular initial value problems. Following their approach, we generalize this class by applying the Nyström method to the initial value problem for an equation of the form y + p(t)y + q(t, y(t)) = 0, t ∈ (0, 1] where p has a certain specified type of singularity and q is sufficiently differentiable, and then we determine the order of convergence. This is followed by computational evidence.

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Nyström method for Cauchy singular integral equations with negative index
✍ M.C. De Bonis; C. Laurita 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 839 KB

In this paper, the authors propose a Nyström method to approximate the solutions of Cauchy singular integral equations with constant coefficients having a negative index. They consider the equations in spaces of continuous functions with weighted uniform norm. They prove the stability and the conver