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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.