Solution of nonlinear PDE ║u║=c over a general space curve

Abstract

A method has been presented for finding the solution surface of the NPDE: u  c , bounded by a general space curve. The method is based on the geometric characteristics of the surface, and is called the “Cone-Slot Method". It has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. An algorithm has been suggested on the basis of mathematics of these considerations. In previous methods the boundary curve had to be level. They obtain the surface as an assembly of its contour curves. In this method however, the solution surface is obtained as an assembly of its characteristics. The boundary curve can also be a general unlevel skew space curve. The method requires no mesh for calculation and allows the area of the integral surface and underneath volume to be readily determined.