New direct method to solve nonlinear Volterra-Fredholm integral and integro-differential equations using operational matrix with block-pulse functions

Progress In Electromagnetics Research B

Volumn 8, Issue , 2008, Pages 59-76

  Babolian, E ^a   Masouri, Z ^b   Hatamzadeh Varmazyar, S ^b  

^a KHARAZMI UNIVERSITY   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL EFFICIENCY; INTEGRODIFFERENTIAL EQUATIONS; MATRIX ALGEBRA; NONLINEAR SYSTEMS; NUMERICAL METHODS;

ALGEBRAIC EQUATIONS; BLOCK-PULSE FUNCTION; ERROR EVALUATION; NUMERICAL SOLUTION; OPERATIONAL MATRICES; OPERATIONAL MATRIX OF INTEGRATION; PROJECTION METHOD; VOLTERRA-FREDHOLM;

NONLINEAR EQUATIONS;

EID: 67349243787     PISSN: 19376472     EISSN: None     Source Type: Journal    
DOI: 10.2528/pierb08050505     Document Type: Article

References (42)

1. Arnold, M. D., "An efficient solution for scattering by a perfectly conducting strip grating, " Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 891-900, 2006
2. Zhao, J. X., "Numerical and analytical formulations of the extended MIE theory for solving the sphere scattering problem, " Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 967-983, 2006
3. Rui, P.-L. and R. Chen, "Implicity restarted gmres fast Fourier transform method for electromagnetic scattering, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 7, 973-976, 2007
4. Wang, M. Y., J. Xu, J. Wu, Y. Yan, and H.-L. Li, "FDTD study on scattering of metallic column covered by doublenegative metamaterial, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1905-1914, 2007
5. Liu, X.-F., B. Z. Wang, and S.-J. Lai, "Element-free Galerkin method in electromagnetic scattering field computation, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1915-1923, 2007
6. Kumar, P., T. Chakravarty, S. Bhooshan, S. K. Khah, and A. De, "Numerical computation of resonant frequency of gap coupled circular microstrip antennas, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 10, 1303-1311, 2007
7. Ding, W., L. Chen, and C. H. Liang, "Numerical study of Goos-Hänchen shift on the surface of anisotropic left-handed materials, " Progress In Electromagnetics Research B, Vol. 2, 151-164, 2008
8. Popov, A. V. and V. V. Kopeikin, "Electromagnetic pulse propagation over nonuniform earth surface: Numerical simulation, " Progress In Electromagnetics Research B, Vol. 6, 37-64, 2008
9. Suyama, T., Y. Okuno, A. Matsushima, and M. Ohtsu, "A numerical analysis of stop band characteristics by multilayered dielectric gratings with sinusoidal profile, " Progress In Electromagnetics Research B, Vol. 2, 83-102, 2008
10. Mokari, H. and P. Derakhshan-Barjoei, "Numerical analysis of homojunction Gallium arsenide avalanche photodiodes (GAAs-APDs), " Progress In Electromagnetics Research B, Vol. 7, 159-172, 2008
11. Steinbauer, M., R. Kubasek, and K. Bartusek, "Numerical method of simulation of material influences in MR tomography, " Progress In Electromagnetics Research Letters, Vol. 1, 205-210, 2008
12. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, E. Babolian, and Z. Masouri, "Numerical approach to survey the problem of electromagnetic scattering from resistive strips based on using a set of orthogonal basis functions, " Progress In Electromagnetics Research, PIER 81, 393-412, 2008
13. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, and Z. Masouri, "A moment method simulation of electromagnetic scattering from conducting bodies, " Progress In Electromagnetics Research, PIER 81, 99-119, 2008
14. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, E. Babolian, and Z. Masouri, "Calculating the radar cross section of the resistive targets using the Haar wavelets, " Progress In Electromagnetics Research, PIER 83, 55-80, 2008
15. Hatamzadeh-Varmazyar, S. and M. Naser-Moghadasi, "New numerical method for determining the scattered electromagnetic fields from thin wires, " Progress In Electromagnetics Research B, Vol. 3, 207-218, 2008
16. Hatamzadeh-Varmazyar, S. and M. Naser-Moghadasi, "An integral equation modeling of electromagnetic scattering from the surfaces of arbitrary resistance distribution, " Progress In Electromagnetics Research B, Vol. 3, 157-172, 2008
17. Jiang, G.-X., H.-B. Zhu, and W. Cao, "Implicit solution of modified form of time-domain electric field integral equation, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 5, 697-707, 2007
18. Franceschini, G., A. Abubakar, T. M. Habashy, and A. Massa, "A comparative assessment among iterative linear solvers dealing with electromagnetic integral equations in 3D inhomogeneous anisotropic media, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 7, 899-914, 2007
19. Wu, C. and G.-X. Jiang, "Stabilization procedure for the timedomain integral equation, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 11, 1507-1512, 2007
20. Tong, M. S., "A stable integral equation solver for electromagnetic scattering by large scatterers with concave surface, " Progress In Electromagnetics Research, PIER 74, 113-130, 2007
21. Hussein, K. F. A., "Fast computational algorithm for EFIE applied to arbitrarily-shaped conducting surfaces, " Progress In Electromagnetics Research, PIER 68, 339-357, 2007
22. Maleknejad, K. and M. Hadizadeh, "The numerical analysis of Adomian's decomposition method for nonlinear Volterra integral and integro-differential equations, " International Journal of Engineering Science, Iran University of Science & Technology, Vol. 8, No. 2a, 33-48, 1997
23. Wazwaz, A. M., A First Course in Integral Equations, World Scientific, Singapor, 1997
24. Akyüz-Daşcioğlu, A., "A Chebyshev polynomial approach for linear Fredholm-Volterra integro-differential equations in the most general form, " Appl. Math. Comput., Vol. 181, 103-112, 2006
25. Brunner, H., Collocation Method for Volterra Integral and Relation Functional Equations, Cambridge University Press, Cambridge, 2004
26. Delves, L. M. and J. L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, Cambridge, 1985
27. Maleknejad, K. and H. Derili, "The collocation method for Hammerstein equations by Daubechies wavelets, " Appl. Math. Comput., Vol. 172, 846-864, 2006
28. Maleknejad, K., M. Karami, and M. Rabbani, "Using the Petrov-Galerkin elements for solving Hammerstein integral equations, " Appl. Math. Comput., Vol. 172, 831-845, 2006
29. Maleknejad, K. and Y. Mahmoudi, "Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations, " Appl. Math. Comput., Vol. 145, 641-653, 2003
30. Babolian, E. and Z. Masouri "Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions, " Journal of Computational and Applied Mathematics, in press, 2007, doi: 10.1016/j.cam.2007.07.029
31. Babolian, E. and A. Salimi Shamloo "Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions, " Journal of Computational and Applied Mathematics, Vol. 214, 495-508, 2008
32. Xu, L., Y.-C. Guo, and X.-W. Shi, "Dielectric half space model for the analysis of scattering from objects on ocean surface, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2287-2296, 2007
33. Zhong, X. J., T. Cui, Z. Li, Y.-B. Tao, and H. Lin, "Terahertzwave scattering by perfectly electrical conducting objects, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2331-2340, 2007
34. Li, Y.-L., J.-Y. Huang, and M.-J. Wang, "Scattering cross section for airborne and its application, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2341-2349, 2007
35. Wang, M. Y., J. Xu, J. Wu, Y. Yan, and H.-L. Li, "FDTD study on scattering of metallic column covered by doublenegative metamaterial, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1905-1914, 2007
36. Liu, X.-F., B. Z. Wang, and S.-J. Lai, "Element-free Galerkin method in electromagnetic scattering field computation, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1915-1923, 2007
37. Du, P., B. Z. Wang, H. Li, and G. Zheng, "Scattering analysis of large-scale periodic structures using the sub-entire domain basis function method and characteristic function method, " Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 2085-2094, 2007
38. Tuz, V. R., "Three-dimensional Gaussian beam scattering from a periodic sequence of bi-isotropic and material layers, " Progress In Electromagnetics Research B, Vol. 7, 53-73, 2008
39. Sukharevsky, O. I. and V. A. Vasilets, "Scattering of reflector antenna with conic dielectric radome, " Progress In Electromagnetics Research B, Vol. 4, 159-169, 2008
40. Wang, M.-J., Z.-S. Wu, and Y. L. Li, "Investigation on the scattering characteristics of Gaussian beam from two dimensional dielectric rough surfaces based on the Kirchhoff approximation, " Progress In Electromagnetics Research B, Vol. 4, 223-235, 2008
41. Sun, X. and H. Ha, "Light scattering by large hexagonal column with multiple densely packed inclusions, " Progress In Electromagnetics Research Letters, Vol. 3, 105-112, 2008
42. Kokkorakis, G. C., "Scalar equations for scattering by rotationally symmetric radially inhomogeneous anisotropic sphere, " Progress In Electromagnetics Research Letters, Vol. 3, 179-186, 2008