Numerical approximation of linear operator equations using a generalized Fourier series: Ordinary and partial differential equations with boundary conditions (Q918639)

The authors propose the numerical solution of boundary problems \(Lu=g_ 1\text{ in } \Omega,\) \(Bu=g_ 2\text{ on } \partial \Omega,\) where L is a linear differential operator in \(\Omega\) and B a linear boundary operator, by the classical least squares method. By using an orthonormal set of basis functions (obtained by the Gram-Schmidt procedure), the normal equations are solved directly by integral formulae (`generalized Fourier coefficients'). The method is applied to a two-dimensional model for coupled heat and soil water transport in algid soils.