Approximate numerical solutions $y(x)$ of nonhomogeneous linear
difference equations on an interval [-1,1] are proposed to be
sought in the form of expansions in terms of Legendre polynomials.
A very routine exercise, with many formulae displayed but with no
theoretical analysis of errors offered. Maple 9 is used to
illustrate this virtually elementary idea by four examples of the
first and second order with constant coefficients. In this sense
the title (which contains the words like ``matrix method",
``higher-order", ``mixed argument" and ``hybrid polynomials") is
unbelievably misleading.


MR2277328 Gülsu, Mustafa; Sezer, Mehmet; Tanay, Bekir A matrix
method for solving high-order linear difference equations with
mixed argument using hybrid Legendre and Taylor polynomials. J.
Franklin Inst. 343 (2006), no. 6, 647--659. 65Q05 (39A10)