Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational ...

In this talk we present few instances of multilevel approximation methods involving PDEs with random parameters and associated scalar output quantities of interest (QoI). Multilevel methods aim at ...

\(\ds dV=\frac{72}{\pi^2}\text{.}\) Observe that \(\ds dr=\frac{1}{8\pi}\text{.}\) Observe that \(\Delta A=A(s+\Delta s)-A(s)=2s\Delta s+(\Delta s)^2\) and \(dA=2s ...

Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and ...

A new study provides a rigorous theoretical and numerical analysis of the accuracy of the method of characteristics (MoC), a ...

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply ...