Numerical solution of inverse problems in hydrodynamics

Numerical solution of inverse Sturm–Liouville problems

A new algorithm is proposed for solving the inverse Sturm–Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov’s method instead of the second order method of the related algorithm of Fabiano, Knobel and Lowe. An extension by Andrew and Paine of the asymptotic correction technique of Paine, de Hoog and Anderssen is the key to the success of the new algorith...

Multi-Level Approach to Numerical Solution of Inverse Problems

Mathematical modeling of an engineering system often leads to such formulations for which one can not obtain a closed form solution/analysis, and thus numerical methods are to be used. In the process, we need to transform the system from an infinite dimensional space to a finite dimensional one(discretization). The result is usually a system of linear equations[5] for which the linear least squ...

Numerical Solution of Limited-data Inverse Problems Arising from X-ray Tomography and Acoustic Inverse Scattering

Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics

We discuss the numerical treatment of a nonlinear second order boundary value problem in ordinary differential equations posed on an unbounded domain which represents the density profile equation for the description of the formation of microscopical bubbles in a non-homogeneous fluid. For an efficient numerical solution the problem is transformed to a finite interval and polynomial collocation ...

Inverse Problems Light: Numerical Differentiation

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