In this paper we study the linearizability problem of the two-dimensional complex quasi-cubic system ż = z + (zw)(a30z + a21zw + a12zw + a03w), ẇ = −w − (zw)(b30w + b21wz+b12wz +b03z), where z,w, ai j, bi j ∈ C and d is a real number. We find a transformation to change the quasi-cubic system into an equivalent quintic system and then obtain the necessary and sufficient linearizability condition...

A method based on innnite parameter conservation laws is described to factor linear differential operators out of nonlinear partial diierential equations (PDEs) or out of diierential consequences of nonlinear PDEs. This includes a complete linearization to an equivalent linear PDE (system) if that is possible. Innnite parameter conservation laws can be computed, for example, with a computer alg...

Equivalent Linearization and Monte Carlo Simulation are the most important techniques in analyzing large non-linear structural systems under random excitation. This paper reviews the development and the state-of-the-art of Equivalent Linearization and Monte Carlo Simulation in stochastic structural dynamics. General Remarks An extensive benchmark study [114] has revealed that most of the comput...

The relative performance of a non-linear FAS multigrid algorithm and an equivalent linear multigrid algorithm for solving two di erent non-linear problems is investigated. The rst case consists of a transient radiation-di usion problem for which an exact linearization is available, while the second problem involves the solution of the steady-state Navier-Stokes equations, where a rst-order disc...

This paper reports an analytical method to obtain approximate solution for optimal design of tuned inerter damper (TID) in MDOF damped civil structures. The is based on the equivalent linearization which converts mass-stiffness-damping system into a mass-equivalent stiffness and technique modal subsystem structure-TID SDOF system. procedures systems are introduced. Following this, proposed veri...

The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. analysis based on the linearization method which takes form an SOR iteration a positive semidefinite Hessian can be studied in corresponding quotient geometry equivalent representations. In case, optimal relaxation parameter accelerating determined from rate stan...