Dealing with Functional Coefficients Within Tau Method
- 28 Downloads
The spectral tau method was originally proposed by Lanczos for the solution of linear differential problems with polynomial coefficients. In this contribution we present three approaches to tackle integro-differential equations with non-polynomial coefficients: (i) making use of functions of matrices, (ii) applying orthogonal interpolation and (iii) solving auxiliary differential problems by the tau method itself. These approaches are part of the Tau Toolbox efforts for deploying a numerical library for the solution of integro-differential problems. Numerical experiments illustrate the use of all these polynomial approximations in the context of the tau method.
KeywordsSpectral methods Initial and boundary value problems Software
Mathematics Subject Classification68N01 68N19 65L05 65L10 47G20 34K28
Unable to display preview. Download preview PDF.
- 10.Vasconcelos, P.B., Matos, J., Trindade, M.S.: Spectral Lanczos’ tau method for systems of nonlinear integro-differential equations. In: Constanda, C., et al. (eds.) Integral Methods on Science and Engineering: Theoretical Techniques, vol. 1, pp. 305–314. Springer, Berlin (2017)Google Scholar
- 13.Parlett, B.: Computation of Functions of Triangular Matrices. Memorandum ERL-M481. Electronics Research Laboratory, College of Engineering, University of California, Berkeley (1974)Google Scholar