Fitting And Joint Of Solution Curves Of ODEs

Curve reconstruction is one of the important issues in geometric modeling. There are many methods based on the interpolation and approximation such as Bezier method, B-spline method, NURBS method, subdivision method, etc. Because there are a lot of geometry problems in the fields of physics, chemistry, fluid mechanics, materials science etc. which can be descripted by differential equations. This thesis uses a model of the ordinary differential equation to represent curves.Based on some discrete data points, we consider several algorithms to fitting these data points by using ODEs. (1) By the trapezoid formula of numerical integration, we propose an integration fitting model and the equivalent integral form of the ODEs; (2) In order to satisfy end interpolation condition of the fitting curve, we add the interpolation constraints to the integration fitting model, we get the integral correction model with the quasi-interpolation constraints; (3) We combine the first-order and the second-order systems to a mixed model to reach the end interpolation exactly; (4) Based on the previous algorithms,we apply the piecewise fitting strategy to further improve the fitting accuracy.