Numerical simulation of chaotic dynamical systems by the method of differential quadrature

In this paper, the differential quadrature (dq) method is employed to solve some nonlinearchaotic systems of ordinary differential equations (odes). here, the method is applied to chaotic lorenz,chen, genesio and r?ssler systems. the first three chaotic systems are described by three-dimensionalsystems of odes while the last hyperchaotic system is a four-dimensional system of odes. it is foundthat the dq method is unconditionally stable in solving first-order odes. but, care should be taken tochoose a time step when applying the dq method to nonlinear chaotic systems. similar to all conventionalunconditionally stable time integration schemes, the unconditionally stable dq time integration schememay also be possible to produce inaccurate results for nonlinear chaotic systems with an inappropriatelytoo large time step sizes. numerical comparisons are made between the dq method and the conventionalfourth-order rungekutta method (rk4). it is revealed that the dq method can produce better accuracythan the rk4 using larger time step sizes.