| Paper title: |
Approximate solution of high-order integro-differential equations using radial basis functions |
| DOI: | https://doi.org/10.4316/JACSM.201702004 |
| Published in: | Issue 2, (Vol. 11) / 2017 |
| Publishing date: | 2017-10-13 |
| Pages: | 26-29 |
| Author(s): | MAADADI Asma, MEROUANI Abdelbaki, RAHMOUNE Azedine |
| Abstract. | In this paper, we present a numerical method to solve linear and nonlinear high-order Volterra integro-differential equations. This method is based on interpolating by radial basis functions, using Legendre-Gauss-Lobatto nodes and weights. The proposed method reduces the main problem to linear or nonlinear system of algebraic equations. Some numerical examples illustrate the efficiency of the presented method |
| Keywords: | High-order Integro-differential Equations, Radial Basis Functions, Collocation Method, Legendre-Gauss-Lobatto Nodes And Weights |
| References: | 1. L.M. Delves, J.L. Mohamed, Computational methods for integral equations, Cambridge University Press, 1985. 2. A.M. Wazwaz, Linear and nonlinear integral equations Methods and applications, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2011. 3. A. Akyüz-Daşcoğlu, M. Sezer (2005), Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations, Journal of Franklin Institute, Vol. 342, pp. 688-701. 4. S. Yalçinbaş, M. Sezer, H.H. Sorkun (2009), Legendre polynomial solutions of high-order linear Fredholm integro-differential equations, Applied Mathematics and Computation, Vol. 210, pp. 334-349. 5. K. Maleknejad, Y. Mahmoudi (2003), Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations, Applied Mathematics and Computation. Vol. 145, pp. 641-653. 6. H. Aminikhah, S. Hosseini, J. Alavi (2015), Approximate analytical solution for high-order integro-differential equation by Chebyshev Wavelets, Information Sciences Letters, Vol. 4, No. 1, pp. 31-39. 7. R.S. Chandel, A. Singh, D. Chouhan (2015), Solution of higher order Volterra integro-differential equations by Legendre Wavelets, International Journal of Applied Mathematics, Vol. 28, No. 4, pp. 377-390. 8. S.G. Venkatesh, S.K. Ayyaswamy, S. Raja Balachandar (2012), Legendre approximation solution for a class of higher-order Volterra integro-differential equations, Ain Shams Engineering Journal, Vol. 3, pp. 417-422. 9. A.H. Bhrawy, E. Tohidi, F. Soleymani (2012), A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals, Applied Mathematics and Computation, Vol. 219, pp. 482-497. 10. J. Biazar, M.A. Asadi (2015), Indirect RBF for high-order integro-differential equations, British Journal of Mathematics and Computer Science, Vol. 11, pp. 1-16. 11. A. Golbabai, S. Seifollahi (2007), Radial basis function networks in the numerical solution of linear integro-differential equations, Applied Mathematics and Computation, Vol. 188, pp. 427-432. 12. K. Parand, S. Abbasbandy, S. Kazem, J.A. Rad (2011), A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation, Commun Nonlinear Sci Numer Simulat, Vol. 16, pp. 4250-4258. 13. A.M. Wazwaz (2001), A reliable algorithm for solving boundary value problems for higher-order integro-differential equations, Applied Mathematics and Computation, Vol. 118, No. 23, pp. 327-342. 14. J. Zhao (2013), Compact finite difference methods for high order integro-differential equations, Applied Mathematics and Computation, Vol. 221, pp. 66-78. 15. R.P. Agarwal, Boundary value problems for high ordinary differential equations, World Scientific, Singapore, 1986. 16. W. Chen, Z.J. Fu, C.S. Chen, Recent Advances in Radial Basis Function Collocation Methods, Springer, 2014. 17. M.D. Buhmann, Multivariable interpolation using radial basis functions, PhD thesis, University of Cambridge, 1989. 18. M.D. Buhmann, Radial basis functions: theory and implementations, Cambridge University Press, 2003. 19. I.R.H. Jackson, Radial basis function methods for multivariable approximation, PhD thesis, University of Cambridge, 1988. 20. R. Schaback (1996), Approximation by radial basis functions with finitely many centers, Constructive Approximation, Vol. 12, No. 3, pp. 331-340. 21. H. Wendland (1998), Error estimates for interpolation by compactly supported radial basis functions of minimal degree, Journal of Approximation Theory, Vol. 93, No. 2, pp. 258-272 |
| Back to the journal content | |
