Numerical and asymptotic solution of a sixth-order nonlinear diffusion equation and related coupled systems

This paper proposes a numerical method to solve for the moving boundary given by a beam of negligible mass on the surface of a thin film. The model leads to a sixth-order equation which is discretized in a way that readily represents the minimization of strain energy and conservation of mass. The di...

Mô tả đầy đủ

Chi tiết về thư mục
Những tác giả chính: Smith, W, Howison, S, Mayers, D
Định dạng: Journal article
Ngôn ngữ:English
Được phát hành: 1996
Miêu tả
Tóm tắt:This paper proposes a numerical method to solve for the moving boundary given by a beam of negligible mass on the surface of a thin film. The model leads to a sixth-order equation which is discretized in a way that readily represents the minimization of strain energy and conservation of mass. The discretized system is then coupled together and linearized via Newton's method. The Jacobian matrix is solved by using an appropriate algorithm, depending on the constraints and matrix structure.