Numerical Methods of Nonlinear Problems

Majority of phenomena in science and engineering can be mathematically described by either linear or nonlinear, often partial differential equation (PDE) models. As the solutions to the underlying application problems largely depend on the solutions to their mathematical models, solving these PDE models numerically has been critically important for the resolutions of these scientific and engineering problems. Despite its importance in sciences, the study for numerical methods in nonlinear problems is far from mature. There is an urgent need for communication between different disciplines for nonlinear problems including pure mathematicians, engineers, as well as numerical analysts. The workshop aims at bringing together researchers and scientists including post-docs and graduate students to exchange and stimulate ideas in numerical solutions for nonlinear problems, with a special focus on novel approaches and new directions for nonlinear PDEs. Techniques from a number of research areas including geometry, machine learning, non-local calculus, partial differential equation theory and numeric would make this workshop a real inter-disciplinary one with promising industrial applications. For this workshop, we will put emphasis to include techniques related to: 1) recent development in theory for nonlinear PDEs, 2) nonlinear calculus, 3) cutting-edge numerical techniques in solving nonlinear problems.