Two Efficient Approaches Based on Radial Basis Functions to Nonlinear Time-dependent Partial Differential Equations
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Authors
Jafar Biazar
- Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
Mohammad Hosami
- Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
Abstract
In this paper, two numerical meshless approaches, based on radial basis functions (RBFs) are
applied to solve nonlinear time-dependent partial differential equations. Both of these approaches are
based on Kansa meshless method. In these procedures the time is descritized to small time steps, the
space is also descritized in each sub-domain. Then by the Kansa collocation method, by using RBFs,
the approximate solution, in each step, is obtained. In the first approach, the nonlinear terms are
eliminated, by linearization. In the second approach nonlinear equations are solved directly, by Fix
point method. Four examples are provided to illustrate the efficiency and the reliability of these
approaches. The results are also compared with each other.
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ISRP Style
Jafar Biazar, Mohammad Hosami, Two Efficient Approaches Based on Radial Basis Functions to Nonlinear Time-dependent Partial Differential Equations, Journal of Mathematics and Computer Science, 9 (2014), no. 1, 1-11
AMA Style
Biazar Jafar, Hosami Mohammad, Two Efficient Approaches Based on Radial Basis Functions to Nonlinear Time-dependent Partial Differential Equations. J Math Comput SCI-JM. (2014); 9(1):1-11
Chicago/Turabian Style
Biazar, Jafar, Hosami, Mohammad. "Two Efficient Approaches Based on Radial Basis Functions to Nonlinear Time-dependent Partial Differential Equations." Journal of Mathematics and Computer Science, 9, no. 1 (2014): 1-11
Keywords
- Meshless Methods
- Radial Basis functions
- Time-dependent nonlinear partial differential equations
MSC
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