A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics

DOI10.1007/s00466-017-1377-4zbMath1398.65195OpenAlexW2581548331WikidataQ113327436 ScholiaQ113327436MaRDI QIDQ1705164

Satya N. Atluri, Xuechuan Wang

Publication date: 14 March 2018

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-017-1377-4

zbMATH Keywords

collocation methodchaosChebyshev polynomialsstrongly nonlinear systemvariational iteration method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items

Bifurcation analysis of stick-slip vibration in a 2-DOF nonlinear dynamical system with dry friction ⋮ Combination of the variational iteration method and numerical algorithms for nonlinear problems ⋮ Bifurcation \& chaos in nonlinear structural dynamics: novel \& highly efficient optimal-feedback accelerated Picard iteration algorithms

Uses Software

• Matlab

Cites Work

• A novel harmonic balance analysis for the van der Pol oscillator
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• A review of the decomposition method in applied mathematics
• A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators
• Homotopy perturbation method for solving boundary value problems
• Advances in Computational Dynamics of Particles, Materials and Structures
• A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation, and its Equivalence to the High Dimensional Harmonic Balance Method: Subharmonic Oscillations
• Computational Methods in Engineering: A Variety ofPrimal & Mixed Methods, with Global & LocalInterpolations, for Well-Posed or Ill-Posed BCs
• A Simple, Fast, and Accurate Time-Integrator for StronglyNonlinear Dynamical Systems
• A Scalar Homotopy Method for Solving an Over/Under-Determined System of Non-Linear Algebraic Equations
• An Iterative Algorithm for Solving a System of Nonlinear Algebraic Equations, F ( x )= 0 , Using the System of ODEs with an Optimum a in d x = l [ a F +(1 - a ) B T F ; B ij =dF i /dx j]
• On solving the initial-value problems using the differential transformation method

This page was built for publication: A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics