GENERALIZED COLLOCATION METHODS FOR TIME-DEPENDENT, NONLINEAR BOUNDARY-VALUE PROBLEMS.

This paper briefly describes the development of generalized collocation methods for solving coupled systems of nonlinear, one-dimensional, parabolic, partial differential equations. The methods are applied to several problems that are representative of fluid flow in a porous medium. The numerical results for the problems solved indicate that collocation methods using C**1 piecewise polynomials with Gauss-Legendre collocation points are more efficient than conventional, second-order, finite-difference methods.