A convolutional-iterative solver for nonlinear dynamical systems

In this paper, a new solver is developed to obtain the solution of nonlinear dynamical systems. The method is based on alternative field equations in which the convolution product appears in place of dot products. The technique is higher-order accurate in the sense that the accuracy is not lost by increasing the time-step, conserving constants of motion. Several examples, including bilinear hardening and softening mass–spring systems and a nonlinear elastic pendulum, are considered to show the validity of the new method.