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 ...

Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical ...

A mathematician has developed new methods for the numerical solution of ordinary differential equations. These so-called multirate methods are highly efficient for large systems, where some components ...

My research interests are in applied and computational mathematics. I am interested in developing and analyzing high-order numerical methods for solving partial differential equations and fractional ...

The paper is intended to give a survey on the state-of-the-art of extrapolation methods for initial value problems in ordinary differential equation systems. All basic discretizations, which are ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Mathematics of Computation, Vol. 33, No. 148 (Oct., 1979), pp. 1251-1256 (6 pages) A polynomial representation of the hybrid methods for solving ordinary differential equations is presented. The ...

Continuation of APPM 4650. Examines numerical solution of initial-value problems and two-point boundary-value problems for ordinary differential equations. Also looks at numerical methods for solving ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Analysis and application of numerical methods for solving large systems of linear equations, which often represent the bottleneck when computing solutions to equations arising in fluid mechanics, ...