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

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 ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Learn how to solve differential equations using Euler and Runge-Kutta 4 methods! This tutorial compares both techniques, explaining accuracy, step size, and practical applications for physics and ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

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 ...

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 ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

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, ...