The Use of Parameter Identification in Error Estimation

J.I. Frankel and K. Taira (USA)


Error analysis, parameter estimation, function decomposition


In a recent study, the authors developed a novel mathematical framework for investigating steady, laminar, radially accelerating or decelerating flows confined be tween two parallel flat disks. This flow is normally described by a nonlinear, second-order, boundary-value problem containing an unknown parameter. The system is adjoined to an integral constraint in order to uniquely determine this parameter. In the course of that investigation, an unusual nonlinear differential equation was constructed for the local error occurring at each approximation level in the collocation solution of the equivalent Hammerstein-Fredholm formulation. The resulting nonlinear differential equation contained the second derivative of the unknown error at an end point. This paper presents a novel application and numerical approach for resolving the local error distribution using a parameter estimation viewpoint. This viewpoint is computationally efficient and accurate.

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