Solution of Basset integro-differential equations by IIR digital filters

Abstract

A new O(n) time complexity numerical method for computing the solutions of Basset integro-differential equations is presented. The method is based on the use of Laplace and bilinear transformations, leading after a precise Chebyshev rational interpolation, to the construction of first order infinite impulse response (IIR) filters. The resulting recurrence relations allow for a very accurate O(n) resolution of Basset equations. Different numerical examples are presented in order to demonstrate the applicability of the method to the study of the transient creeping flow motion of a rigid spherical particle. The results are compared on the one hand to those provided by the Talbot inversion method and on the other hand to those provided by an iterative method specially elaborated here to solve the Basset problem.

Keywords

• Integro-differential equations
• Basset kernel
• Laplace transformation
• Infinite impulse response filters
• Piecewise linear approximation