Higher derivative explicit one step methods for non‐linear dynamic problems. Part I: Design and theory

Abstract

A new higher order explicit one step scheme is presented for use in the,solution of a certain class of nonlinear problems in structural dynamics. The generalized scheme covers some recently developed multistep algorithms as well as some new one step methods with improved numerical properties. A weighted residual approach is used which contains new aspects for design of single step algorithms. Accuracy and stability are investigated for linear and non-linear systems. Algorithms with higher accurary than the central difference method are developed and optimized to minimize the reduction in the stability limit.

Explicit Predictor–multicorrector Time Discontinuous Galerkin Methods for Linear Dynamics

“…Thereby, the development of suitable solution algorithms for equations (9) is a critical issue in the practical application of the method. 3. THE EXPLICIT PREDICTOR}MULTICORRECTOR METHOD 3.1.…”

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Parallel Algorithms for Fourth-Order Parabolic Equations

“…. and it is this recurrence relation which will be used in the development of the parallel algorithms for solving the initialboundary-value problem (1)- (5). It will not be necessary to compute B or A-' explicitly.…”

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