At the beginning of this decade, a deep understanding of partial differential equations (PDEs) occupies a crucial place in scientific and technological advancements. Numerical analysis plays a key role in the practical resolution of these complex equations, which model various natural and industrial phenomena, such as diffusion, fluid mechanics, or thermal transfer. The use of … Read more
Spectral methods represent a revolutionary approach in the field of numerical approximation, particularly valued for their exceptional accuracy in solving differential equations. Based on the use of suitable basis functions, particularly orthogonal polynomials, they exploit the richness of the spectrum of functions to achieve an efficient representation of solutions. This method stands out for its … Read more
Orthogonal polynomials are at the heart of many advancements in numerical analysis and functional approximation. These mathematical tools allow for the precise representation of complex functions while controlling the error associated with this approximation. More than just a theoretical concept, they find practical applications in the calculation of numerical integrals, the solving of linear systems, … Read more