A robust and reliable approach to nonlinear dynamical problems

• Published in: Computer physics communications Vol. 111; no. 1; pp. 87 - 92
• Main Authors: Wei, G.W., Zhang, D.S., Kouri, D.J., Hoffman, D.K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.1998; Elsevier Science
• Subjects: Computational techniques; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Mathematical methods in physics; Nonlinear waves and nonlinear wave propagation (including parametric effects, mode coupling, ponderomotive effects, etc.); Nonlinearity (including bifurcation theory); Physics; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Waves, oscillations, and instabilities in plasmas and intense beams; 52.35.Mw; 02.70.Rw; 47.20.Ky; Korteweg-de Vries equation; Partial differential equations; Theoretical study; Gaussian distribution; Fokker-Planck equation; Nonlinear dynamical systems; Function approximation; Burgers equation
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(98)00020-4

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.