In this paper, Chebyshev and Legendre approximations are proposed for estim
ating parameters in differential equations, which are easy to be performed.
The convergence and the spectral accuracy are proved, even without some co
nditions as imposed in other papers. The numerical results show the advanta
ges of this new approach. (C) 1999 Elsevier Science Inc. All rights reserve
d. AMS Classification: 34A55; 65L10; 65L99.