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Finite integration method for partial differential equations |
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| Authors: | P.H. Wen Y.C. Hon M. Li T. Korakianitis |
| Affiliation: | 1. School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS, UK;2. Department of Mathematics, City University of Hong Kong, Hong Kong Special Administrative Region;3. College of Mathematics, Taiyuan University of Technology, Taiyuan, China;4. Parks College of Engineering, Aviation and Technology, Saint Louis University, St. Louis, MO 63103, USA |
| Abstract: | A finite integration method is proposed in this paper to deal with partial differential equations in which the finite integration matrices of the first order are constructed by using both standard integral algorithm and radial basis functions interpolation respectively. These matrices of first order can directly be used to obtain finite integration matrices of higher order. Combining with the Laplace transform technique, the finite integration method is extended to solve time dependent partial differential equations. The accuracy of both the finite integration method and finite difference method are demonstrated with several examples. It has been observed that the finite integration method using either radial basis function or simple linear approximation gives a much higher degree of accuracy than the traditional finite difference method. |
| Keywords: | Finite integral method Radial basis functions Partial differential equation Partial differential equation with fractional order Elasto-dynamics Laplace transformation |
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