TY - JOUR
T1 - Finite integration method for solving multi-dimensional partial differential equations
AU - Li, M.
AU - Chen, C. S.
AU - Hon, Y. C.
AU - Wen, P. H.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial Basis Function (RBF) interpolation (uniform/random distributions of nodes) to higher order integration matrices. Using standard time integration techniques, such as Laplace transform, we have shown that the FIM is capable for solving time-dependent partial differential equations. Illustrative numerical examples are given in two-dimension to compare the FIM (FIM-OLA and FIM-RBF) with the finite difference method and point collocation method to demonstrate its superior accuracy and efficiency.
AB - Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial Basis Function (RBF) interpolation (uniform/random distributions of nodes) to higher order integration matrices. Using standard time integration techniques, such as Laplace transform, we have shown that the FIM is capable for solving time-dependent partial differential equations. Illustrative numerical examples are given in two-dimension to compare the FIM (FIM-OLA and FIM-RBF) with the finite difference method and point collocation method to demonstrate its superior accuracy and efficiency.
KW - Finite integration method
KW - Laplace transformation
KW - Partial differential equation
KW - Radial basis functions
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=84930762150&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84930762150&origin=recordpage
U2 - 10.1016/j.apm.2015.03.049
DO - 10.1016/j.apm.2015.03.049
M3 - RGC 21 - Publication in refereed journal
SN - 0307-904X
VL - 39
SP - 4979
EP - 4994
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 17
ER -