Non-standard, explicit integration algorithms based on linearization for nonlinear dynamic response analysis

摘要

Non-standard finite difference methods for initial-value problems of second-order ordinary differential equations based on piecewise linearization are developed. Linearization methods provide piecewise analytical solutions which are globally differentiable, result in explicit finite difference algorithms, and are exact for constant coefficients equations with a right-hand side which depends linearly on time. The accuracy of these methods is assessed by obtaining the solutions of several conservative and dissipative, stiff and non-stiff, regular and chaotic problems, and comparing them with those of the MATLAB ode45 solver, state transition matrix algorithms and non-standard Euler techniques.