SMOOTH SOLUTION OF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTIONS

Z. Avazzadeh; M. Heydari; W. Chen; G. B. Loghmani

doi:10.11948/2014005

2014 Volume 4 Issue 2

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Z. Avazzadeh, M. Heydari, W. Chen, G. B. Loghmani. SMOOTH SOLUTION OF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2014, 4(2): 115-127. doi: 10.11948/2014005

Citation:

Z. Avazzadeh, M. Heydari, W. Chen, G. B. Loghmani. SMOOTH SOLUTION OF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2014, 4(2): 115-127. doi: 10.11948/2014005

SMOOTH SOLUTION OF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTIONS

1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;
2 Department of Mathematics, Yazd University P. O. Box:89195-741 Yazd, Iran

Abstract

Abstract

In this work, we present the method based on radial basis functions to solve partial integro-differential equations. We focus on the parabolic type of integro-differential equations as the most common forms including the "memory" of the systems. We propose to apply the collocation scheme using radial basis functions to approximate the solutions of partial integrodifferential equations. Due to the presented technique, system of linear or nonlinear equations is made instead of primary problem. The method is efficient because the rate of convergence of collocation method based on radial basis functions is exponential. Some numerical examples and investigation of the experimental results show the applicability and accuracy of the method.
- Partial integro-differential equations /
- radial basis functions /
- collocation scheme /
- integration method
MSC: 35R09;45K05;97N50

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References

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