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Displaying similar documents to “Solving an inverse Sturm-Liouville problem by a Lie-group method.”

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

Liubov Efremova, Gerhard Freiling (2013)

Open Mathematics

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We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.

On the solution of inverse problems for generalized oxygen consumption

Denis Constales, Jozef Kačur (2001)

Applications of Mathematics

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We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied. ...

Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

Milena Dimova, Stefka Dimova, Daniela Vasileva (2013)

Open Mathematics

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The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem....

Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values

Alexandre Janon, Maëlle Nodet, Clémentine Prieur (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.