28/02/2002, 10:30 — 11:30 — Room P3.31, Mathematics Building
A. I. Sukov, Moscow State Technological University, Stankin
Numerical Methods for Nonlinear Diferential Equations and Applications to Physics
Short-Course on
Numerical Methods for Nonlinear Diferential Equations and Applications to Physics
1. Numerical Solution of Boundary Value Problems For Nonlinear Ordinary Differential Equations on a Finite Interval
1.1 Linearization method.
1.2 Shooting method.
1.3 Difference pass and differential pass methods.
2. Numerical Solution of Boundary Value Problems for Nonlinear Ordinary Differential Equations on an Infinite Interval
2.1 Example related to electrodynamics: a singular problem for a second-order nonlinear ordinary differential equation.
2.2 Example related to hydrodynamics: a singular problem for a third-order nonlinear ordinary differential equation.
3. Numerical Solution of Boundary Value Problems for Systems of Nonlinear Ordinary Differential Equations on a Finite Interval
3.1 Reduction method applied to Cauchy problems.
3.2 Linearization method.
3.3 Conjugate operator method.
4. Numerical Solution of Boundary Value Problems for Systems of Nonlinear Ordinary Differential Equations on an Infinite Interval
4.1 Example related to hydrodynamics: a flow near a rotating disk of an infinite radius.
4.2 Example related to hydrodynamics: a flow near an immovable infinite base due to a fluid rotation far from the wall (without and in the presence of a magnetic field).
