Numerical Calculation With Arbitrary Precision

Lagrange and the Solution of Numerical Equations

In 1798 J.-L. Lagrange published an extensive book on the solution of numerical equations. Lagrange had developed a general systematic algorithm for detecting, isolating, and approximating all real and complex roots of a polynomial equation with real coeecients, with arbitrary precision. In contrast to Newton's Method, Lagrange's algorithm is guaranteed to converge. We discuss some lesser known...

Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

Nonlinear vibrations of thin rectangular plates are considered, using the von Kármán equations in order to take into account the effect of geometric nonlinearities. Solutions are derived through an expansion over the linear eigenmodes of the system for both the transverse displacement and the Airy stress function, resulting in a series of coupled oscillators with cubic nonlinearities, where the...

CALCULATION OF NON LIFTING POTENTIAL FLOW USING DESINGULARIZED CAUCHY\'S FORMULA

This paper discusses the disturbance velocity and potential as well as the total velocity formulation for non lifting potential flow problem. The problem is derived based on the Cauchy method formulation. The adding and subtracting back technique is used to desingularize the integral equations. The desingularized boundary integral equations are then discretized. The discretized equations can be...

Vibration of Train-Rail-Bridge Interaction Considering Rail Irregularity with Arbitrary Wavelength

A generation method for the rail random irregularity with arbitrary wavelength interval (WI) is developed, and its accuracy and efficiency are demonstrated. Then a moving wheel-rail-bridge interaction element is derived to establish the finite element equations of motion for the train-rail-bridge interaction system, and the flow chart of assembly and calculation for the system equations is give...

Intégration numérique avec erreur bornée en précision arbitraire. (Arbitrary precision numerical integration with bounded error)