Applications of the Tau Method to problems in mathematical modelling: A survey of recent applications of the Tau Method to problems in mathematical modelling

Authors:
Eduardo L. Ortiz
Affiliations:
Imperial College, Mathematics Department, London SW7, England
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1988

Citing 4
Cited 0

Tau-lines: A new hybrid approach to the numerical treatment of crack problems based on the Tau method

Computer Methods in Applied Mechanics and Engineering
Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly

Journal of Computational Physics
Linear recursive schemes associated with some nonlinear partial differential equations in one dimension and the Tau method

SIAM Journal on Mathematical Analysis
The Tau Method

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.98

Visualization

Abstract

New formulations and recent theoretical developments have made it possible to apply the Tau Method to a variety of interesting problems of Engineering Science where a high accuracy is required of the solution. These include strongly nonlinear, stiff and singularly perturbed boundary value problems for ordinary and systems of ordinary differential equations in which the solution may not be unique; boundary value problems for singular and nonlinear partial differential equations; eigenvalue problems for ordinary and partial differential and difference-differential equations where the spectral parameter may enter linearly or nonlinearly in the equation or in the boundary conditions and be real or complex and in the presence of singular perturbation; and to differential inclusions, in connection with problems of control systems design. The problems considered are relevant to field as diverse as elasticity, vibrations theory, fluid flow, fracture mechanics, hydrodynamic stability, electromagnetism, traffic simulations and control theory.