Mathematical Modeling and Analysis

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Numerical method and software for ordinary differential equations (ODE) and differential-algebraic equations (DAE)

• ODE/DAE method expertise includes initial and boundary value problem, stability analysis, structure-preserving (symlectic and Lie-Poisson) integration, error control, optimal control subject to ODE/DAE constraints.
• Explicit and implicit time integration
• Parallel computation
• ODE/DAE software expertise includes adaptive order and stepsize method, general ODE/DAE software development, nonlinear solver, linear solver (direct and Krylov), automatic differentiation, gradient-based optimization; He is the principle developer of general software DASPK3.0.