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A conditionally P-stable fourth-order exponential-fitting method for y″=f(x,y)

✍ Scribed by L.Gr. Ixaru; B. Paternoster

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
130 KB
Volume
106
Category
Article
ISSN
0377-0427

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✦ Synopsis

We search for the modiÿcation of the stability properties of a P-stable multistep algorithm with an order greater than two when this is reformulated on the basis of the exponential ÿtting. We e ectively construct the exponential-ÿtting version of the fourth-order two-step algorithm of Chawla (BIT 21 (1981) 190 -193). In order to characterize the stability properties of the new version, we ÿrst introduce the concept of the conditional P-stability of a family of exponential-ÿtting methods and the parameter  max to be associated to a conditionally P-stable family. We then show that this version is conditionally P-stable indeed, with Âmax = 3:4. This means that the method can be used for sti problems provided some typically nonsevere restrictions are imposed on the stepsize h.

📜 SIMILAR VOLUMES

A new fourth-order method for y″=g(x)y+r
A new fourth-order method for y″=g(x)y+r(x)
✍ John P. Coleman 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 636 KB

A numerical method is proposed for solving linear differential equations of second order without first derivatives. The new method is superior to de Vogelaere's for this class of equations, and for non-linear equations it becomes an implicit extension of de Vogelaere's method. The global truncation