Used extensively in the numerical solution of differential equations, pseudo-spectral methods combine the power of global polynomials with spectral approximation techniques to deliver remarkable accuracy. In 2025, they continue to dominate the field of numerical methods thanks to their ability to handle complex problems with optimized computational costs. Based on polynomial approximation at so-called collocation … Read more
The resolution of complex partial differential equations (PDEs), which are ubiquitous in various scientific and technical fields, today relies predominantly on advanced numerical methods. Among these, the finite element method stands out as an essential pillar of modern numerical analysis. It enables the understanding and solving of problems that once seemed inaccessible, particularly in the … 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