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 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
-L. Fermo and D. Occorsio, A projection method with smoothing transformation for second kind Volterra integral equations. Dolomites Research Notes on Approximation, 14 12-26, 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, 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 different collocation methods combined with regularization techniques are developed to treat a linear model consisting of two integral equations of the first kind.
Other submitted 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, submitted
- P. Díaz de Alba, L. Fermo, Federica Pes, and G. Rodriguez, Minimal-norm RKHS solution of an integral model in geo-electromagnetism, submitted
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.