A Quick Survey of Recent Developments and Applications of the τ-Method

摘要: The τ-method was first conceived by C. Lanczos in 1938 to construct polynomial approximations the solution y of a given problem involving an equation form Dy = P, where P is algebraic and D linear or ordinary differential operator with coefficients, together some suplementary (initial, boundary mixed) conditions. basic idea as follows: With we associate neighbouring one, Dyn + Zm, Zm conveniently chosen perturbation. usually be combination Tchebysheff Legendre polynomials free called τ-parameters, which are determined such way that τ-approximant yn unique perturbed satisfies exactly has recently been made amenable error analysis computer programming E. Ortiz his co-workers at Imperial College, University London. Since then, it successfully applied so many problems Numerical Functional Analysis should no longer call method but philosophy instead. In support this give brief survey theoretical approaches applications emphasis on those authors' recent work numerical treatment equations.