Numerical treatment of Volterra integral equations
Investigating new methods for the numerical solution of Volterra integral equations. Prove convergence and stability results and assess the effectiveness of the method by means of numerical results. My latest publications on this topic are:
-L. Fermo, D. Mezzanotte, and D. Occorsio. On the numerical solution of Volterra integral equations on equispaced nodes. Electronic Transactions on Numerical Analysis (ETNA), 59: 9-23 2023
-T. Diogo, L. Fermo, and D. Occorsio. A projection method for Volterra integral equations in weighted spaces of continuous functions. Journal of Integral Equations and Applications, 34:433–448, 2022
-L. Fermo and D. Occorsio. Weakly singular linear Volterra integral equations: a Nyström method in weighted spaces of continuous functions. Journal of Computational and Applied Mathematics, 406 114001, 2022
-L. Fermo and C. van der Mee, Volterra integral equations with highly oscillatory kernels: a new numerical method with applications. Electronic Transactions on Numerical Analysis (ETNA), 54 333-354, 2021
Numerical methods for singular integral equations
Developing new numerical methods to approximate the solution of integral equations which are classified as "singular" in virtue of the pathologies of the kernel function. My last publication on the topic deals with the Cauchy integral equation on the square:
-L. Fermo, M.G. Russo and G. Serafini, A numerical method for the generalized Love integral equation in 2D. Dolomites Research Notes on Approximation, 14 46-57, 2021 -L. Fermo, M.G. Russo and G. Serafini, Numerical treatment of the generalized Love integral equation. Numerical Algorithms, 86(4) 1769-1789, 2021 -L. Fermo, M.G. Russo and G. Serafini. Numerical Methods for Cauchy Bisingular Integral Equations of the First Kind on the square. Journal of Scientific Computing , 79 103-127, 2019
Numerical treatment of integral models applied to geophisics
Developing efficient algorithms to treat integral models which are widely used in the electromagnetic induction techniques.
In the publication P. Diaz de Alba, L. Fermo, F. Pes, and G. Rodriguez. Regularized minimal-norm solution of an overdetermined system of first kind integral equations. Numerical Algorithms, 92:471–502, 2023 a numerical method which stems from the Riesz representation theorem and operates in a reproducing kernel Hilbert space is developed to treat a linear model consisting of two integral equations of the first kind.
Other papers on the topic are:
- G. P. Deidda, P. Díaz De Alba, L. Fermo, and G. Rodriguez, Time domain electromagnetic response of a conductive and magnetic permeable sphere via exponential sums. 2021 21st International Conference on Computational Science and Its Applications (ICCSA), 71-79, 2021
- P. Díaz de Alba, L. Fermo, Federica Pes, and G. Rodriguez, Minimal-norm RKHS solution of an integral model in geo-electromagnetism. 2021 21st International Conference on Computational Science and Its Applications (ICCSA), 21-28, 2021.
P. Diaz de Alba, L. Fermo, van der Mee and G. Rodriguez. Recovering the electrical conductivity of the soil via a linear integral model. Journal of Computational and Applied Mathematics 352, 132-145, 2019
Quadrature schemes and integral equations
Investigating new quadrature rules with applications to integral equations
In the publication P. Díaz De Alba, L. Fermo, and G. Rodriguez, Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules Numerische Mathematik, 146(4) 699-728, 2020 anti-Gaussian quadrature formulae are considered and applied to second-kind Fredholm integral equations.
Specific Cubature rules are studied in D.D. Djukić, L. Fermo, R. M. Mutavdžić. Averaged cubature schemes on the real positive semiaxis. Numerical Algorithms, 92:545–569, 2023.