𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Stability properties of the Newmark, Houbolt and Wilson θ methods

✍ Scribed by Ian Gladwell; Ruth Thomas

Book ID
102954619
Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
644 KB
Volume
4
Category
Article
ISSN
0363-9061

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper analysis the stability of several methods for obtaining numerical solutions of second‐order ordinary differential equations. The methods are popular in structural and geotechnical engineering applications and are direct, that is they do not require the transformation of the second‐order equation into a first‐order system. They include Newmark's method in both implicit and explicit forms, Wilson's θ‐method, Houbolt's method and some variants on this latter method. We shall examine the stability of the methods when applied to the second‐order scalar test equation

where a and c are real.

📜 SIMILAR VOLUMES

On accuracy, stability and efficiency of
On accuracy, stability and efficiency of the Newmark method with incomplete solution by multilevel methods
✍ Jacob Fish; Wen Chen 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 344 KB 👁 2 views

The use of an incomplete iterative solver aimed at approximating solution of equilibrium equation resulting from the "nite element semidiscretization in space is studied. Our approach is motivated by the fact that: (i) the e!ective sti!ness matrix is well conditioned because of the stabilizing e!ect