Numerical approximation of solutions of functional equations using the Tau Method
Copyright policy )Numerical approximation of solutions of functional equations using the Tau Method
The application of the so called Tau method [see e.g. \textit{E. L. Ortiz}, Comput. Math. Appl. 1, 381-392 (1975; Zbl 0356.65006)] to approximate the solutions of certain functional equations is considered. Finally, a brief description of the Tau method as well as the segmented and rational Tau approximations are presented. Then it is shown that the theory of canonical polynomials developed by Ortiz provides a more direct approach to the solution of some functional equations than that one given by \textit{Y. L. Luke}, \textit{J. Wimp} and \textit{B. Y. Ting} [J. Approximation Theory 32, 211-225 (1981; Zbl 0484.33002)]. Finally, by using the same theory, an approximate solution of the functional equation \(y(x)=y(1/x)\) in \(x>0\) is obtained.
- Imperial College London United Kingdom
functional equations, canonical polynomials, difference equations, Nonlinear ordinary differential equations and systems, General theory of functional-differential equations, Numerical methods for initial value problems involving ordinary differential equations, functional differential equations, Functional equations for real functions, Numerical methods for functional equations, segmented Tau method, Tau method, rational Tau approximations
functional equations, canonical polynomials, difference equations, Nonlinear ordinary differential equations and systems, General theory of functional-differential equations, Numerical methods for initial value problems involving ordinary differential equations, functional differential equations, Functional equations for real functions, Numerical methods for functional equations, segmented Tau method, Tau method, rational Tau approximations
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