Exponentially weighted Legendre-Gauss Tau methods for linear second-order differential equations
We develop a method to solve a class of second-order ordinary differential equations with highly oscillatory solutions. The method consists in combining three different techniques: Legendre-Gauss spectral Tau method, exponential fitting, and coefficient perturbation methods. With our approach, the resulting approximate solutions are expressed in terms of an exponentially weighted Legendre polynomial basis {e(omega nx)L(n)(x); n >= 0}, where omega(n) are appropriately chosen complex numbers. The accuracy and efficiency of the method are discussed and illustrated numerically. (C) 2011 Elsevier Ltd. All rights reserved.
tau method coefficient perturbation legendre polynomials collocation