A robust and reliable approach to nonlinear dynamical problems

A new approach, which utilizes Gaussian Lagrange distributed approximating functionals (LDAFs) for evaluating spatial derivatives to high accuracy is proposed for solving nonlinear dynamical problems. Three different nonlinear problems (Burgers' equation, a nonlinear Fokker-Planck equation and the Korteweg-de Vries equation) are used to demonstrate the usefulness and test the accuracy of the method. It is found that the present approach is robust for a variety of different nonlinear dynamical problems, and, using equivalent parameters, is the most accurate available method for the problems which we have examined.