Abstract
AbstractThis 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.
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