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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 350364, 29 pages
http://dx.doi.org/10.1155/2014/350364
Review Article

A Review on the Modified Finite Point Method

1Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan City 70955, Taiwan
2Department of Civil Engineering, National Taiwan University, Taipei City 10617, Taiwan

Received 29 December 2013; Accepted 30 May 2014; Published 24 July 2014

Academic Editor: Keith Ng

Copyright © 2014 Nan-Jing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objective of this paper is to make a review on recent advancements of the modified finite point method, named MFPM hereafter. This MFPM method is developed for solving general partial differential equations. Benchmark examples of employing this method to solve Laplace, Poisson, convection-diffusion, Helmholtz, mild-slope, and extended mild-slope equations are verified and then illustrated in fluid flow problems. Application of MFPM to numerical generation of orthogonal grids, which is governed by Laplace equation, is also demonstrated.