An Analysis on Moving Mesh Methods for Non-Linear Partial Differential Equations: the Approximate Solution: Improving Efficiency and Accuracy in Solving Non-linear Partial Differential Equations using Moving Mesh Methods (Journal of Advances and Scholarly Researches in Allied Education, 2018)
This study is primarily concerned with the use of moving mesh methods for the approximate solution of non-linear partial differential equations of parabolic type. Such methods have become a popular means for the solution of problems which may contain sharp features that are hard to approximate. Whilst efficiently managing computational overheads. Initially, a novel moving grid technique known as Contour Zoning is discussed. This 'static' method is able to reduce numerical resources by grouping together sets of nodes as a moving contour of the solution.