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 ...

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 ...

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 ...

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 ...

Asymptotic error expansions have been obtained for certain numerical methods for linear Volterra integro-differential equations. These results permit the application ...

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 ...

Traditionally, the subject of numerical analysis is about the design and analysis of algorithms for solving mathematical equations on a digital computer. The idea of modern scientific computing, ...

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 ...