1. Dynamic PDE parametric curves
- Author
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Guo-Qin Zheng, Xu-Zheng Liu, Jiaguang Sun, Xia Cui, Jun-Hai Yong, School of Software (THSS), Tsinghua University [Beijing] (THU), Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, cgcad, Thss, and Tsinghua, Thss
- Subjects
Partial differential equation ,Differential equation ,Applied Mathematics ,Mathematical analysis ,020207 software engineering ,010103 numerical & computational mathematics ,02 engineering and technology ,16. Peace & justice ,[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG] ,Finite difference method ,01 natural sciences ,Interpolation ,PDE surface ,Computational Mathematics ,[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG] ,Ordinary differential equation ,Family of curves ,0202 electrical engineering, electronic engineering, information engineering ,PDE curves ,0101 mathematics ,Parametric equation ,Convergence ,Hyperbolic partial differential equation ,Numerical stability ,Mathematics - Abstract
International audience; Dynamic partial differential equation (PDE) parametric curves which can be expressed as a coupled system of two hyperbolic equations are developed. In curve design, dynamic PDE parametric curves can be modified intuitively and are more flexible than ordinary differential equation (ODE) curves. The calculation of dynamic PDE parametric curves must recur to numerical methods and a three-level finite difference scheme is proposed. Approximation and stability properties for the scheme are proved and convergence property is derived. An example of interpolating PDE curves is presented as an application of dynamic PDE parametric curves.
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