Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

A singularly perturbed linear partial differential equation motivated by the geometrical model for crystal growth is considered. A steepest descent analysis of the Fourier transform solution ...

This paper represents a generalization of the stability result on the Euler-Maruyama solution, which is established in the paper M. Milošević, Almost sure exponential stability of solutions to highly ...

Course on using spectral methods to solve partial differential equations. We will cover the exponential convergence of spectral methods for periodic and non-periodic problem, and a general framework ...

Recall that the solution of the initial-value problem \(y^\prime=ky\text{,}\) \(y(0)=A\text{,}\) is given by \(\ds y=Ae^{kx}\text{.}\) Solve the following problems ...