Numerical Methods for Solving One Dimensional Problems With a Moving Boundary

[摘要] This thesis describes some methods which were employed to compute approximate solutions to partial differential equations with moving boundaries verifying the existing numerical solutions, modifying the techniques and applying them to new problems. The problems considered were the determination of the temperature in melting ice and of the concentration of oxygen diffusion in both one dimensional cartesian and axially symmetric cylindrical coordinates. For the melting ice problem the methods studied included variable time step methods with difference formulae and different methods of calculating the variable time step, and also a transformation to fix the moving boundary using a conventional finite difference technique on the known domain. The diffusion problem had a singularity on the initial boundary. The singularity was treated by using an approximate analytical solution and the numerical solution found by a finite difference method with fixed time and space steps and a Lagrange-type formula near the moving boundary.

[发布机构] University:University of Glasgow

[关键词] Computer science