On a method for solving the inverse Sturm–Liouville problem
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Vladislav V. Kravchenko
Abstract
A method for solving the inverse Sturm–Liouville problem on a finite interval is proposed. It is based on a Fourier–Legendre series representation of the integral transmutation kernel. Substitution of the representation into the Gel’fand–Levitan equation leads to a linear algebraic system of equations and consequently to a simple algorithm for recovering the potential. Numerical illustrations are presented.
Funding source: Consejo Nacional de Ciencia y Tecnología
Award Identifier / Grant number: 284470
Funding statement: Research was supported by CONACYT, Mexico via the project 284470.
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Articles in the same Issue
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- Source identification problems for hyperbolic differential and difference equations
- The Regularized Weak Functional Matching Pursuit for linear inverse problems
- An inversion formula for the transport equation in ℝ3 using complex analysis in several variables
- Non-recombining trinomial tree pricing model and calibration for the volatility smile
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- On a method for solving the inverse Sturm–Liouville problem
- Inverse scattering for the higher order Schrödinger operator with a first order perturbation
- On recovering a Sturm–Liouville-type operator with the frozen argument rationally proportioned to the interval length
- An inverse problem for Sturm–Liouville operators on the half-line with complex weights
- Inverse Sturm–Liouville problems for non-Borg conditions
- Theory and numerical methods for solving inverse and ill-posed problems
Articles in the same Issue
- Frontmatter
- Source identification problems for hyperbolic differential and difference equations
- The Regularized Weak Functional Matching Pursuit for linear inverse problems
- An inversion formula for the transport equation in ℝ3 using complex analysis in several variables
- Non-recombining trinomial tree pricing model and calibration for the volatility smile
- Using Landweber iteration to quantify source conditions – a numerical study
- Shape sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity
- On a method for solving the inverse Sturm–Liouville problem
- Inverse scattering for the higher order Schrödinger operator with a first order perturbation
- On recovering a Sturm–Liouville-type operator with the frozen argument rationally proportioned to the interval length
- An inverse problem for Sturm–Liouville operators on the half-line with complex weights
- Inverse Sturm–Liouville problems for non-Borg conditions
- Theory and numerical methods for solving inverse and ill-posed problems
