Fourier operational matrices of differentiation and transmission: Introduction and applications

Abstract and Applied Analysis

Volumn 2013, Issue , 2013, Pages

  Toutounian, F ^a   Tohidi, Emran ^a   Kilicman, A ^b  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

^b UNIVERSITY PUTRA MALAYSIA   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84877263462     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/198926     Document Type: Article

References (31)

1. Rao G. P., Palaisamy K. R., Walsh stretch matrices and functional differential equations. IEEE Transactions on Automatic Control 1982 27 1 272 276 2-s2.0-0020091225 (Pubitemid 12473995)
2. Hwang C., Shih Y. P., Laguerre series solution of a functional differential equation. International Journal of Systems Science 1982 13 7 783 788
3. Sezer M., Yalçinbaş S., Gülsu M., A Taylor polynomial approach for solving generalized pantograph equations with nonhomogenous term. International Journal of Computer Mathematics 2008 85 7 1055 1063 2-s2.0-46249090052 10.1080/00207160701466784
4. Yalçinbaç S., Aynigül M., Sezer M., A collocation method using Hermite polynomials for approximate solution of pantograph equations. Journal of the Franklin Institute 2011 348 6 1128 1139 2-s2.0-79957616126 10.1016/j.jfranklin.2011.05.003
5. Corrington M. S., Solution of differential and integral equations with walsh functions. IEEE Transactions on Circuit Theory 1973 20 5 470 476 2-s2.0-0015662698
6. Chen C. F., Hsiao C. H., Time-domain synthesis via walsh functions. Proceedings of the Institution of Electrical Engineers 1975 122 5 565 570 2-s2.0-0016509362
7. Chen C. F., Hsiao C. H., Walsh series analysis in optimal control. International Journal of Control 1975 21 6 881 897 2-s2.0-0016521928
8. Hsu N. S., Cheng B., Analysis and optimal control of time-varying linear systems via block-pulse functions. International Journal of Control 1981 33 6 1107 1122 2-s2.0-0019572595 (Pubitemid 12425981)
9. Hwang C., Shih Y. P., Parameter identification via laguerre polynomials. International Journal of Systems Science 1982 13 2 209 217 2-s2.0-0020093063 (Pubitemid 12551256)
10. Horng I. R., Chou J. H., Shifted chebyshev direct method for solving variational problems. International Journal of Systems Science 1985 16 7 855 861 2-s2.0-0022098480
11. Chang R. Y., Wang M. L., Shifted Legendre direct method for variational problems. Journal of Optimization Theory and Applications 1983 39 2 299 307 2-s2.0-0020707935 10.1007/BF00934535 (Pubitemid 13506542)
12. Kekkeris G. T., Paraskevopoulos P. N., Hermite series approach to optimal control. International Journal of Control 1988 47 2 557 567 2-s2.0-0023827017 (Pubitemid 18580866)
13. Razzaghi M., Razzaghi M., Fourier series direct method for variational problems. International Journal of Control 1988 48 3 887 895 2-s2.0-0024069755
14. Doha E. H., Bhrawy A. H., Saker M. A., Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations. Applied Mathematics Letters 2011 24 4 559 565 2-s2.0-78650516844 10.1016/j.aml.2010.11.013
15. Paraskevopoulos P. N., Sklavounos P. G., Georgiou G. C., The operational matrix of integration for Bessel functions. Journal of the Franklin Institute 1990 327 2 329 341 2-s2.0-0025592184
16. Bhrawy A. H., Tohidi E., Soleymani F., A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals. Applied Mathematics and Computation 2012 219 2 482 497 10.1016/j.amc.2012.06.020
17. Akyüz-Dascioglu A., Chebyshev polynomial approximation for high-order partial differential equations with complicated conditions. Numerical Methods for Partial Differential Equations 2009 25 3 610 621 2-s2.0-66049138616 10.1002/num.20362
18. Gülsu M., Gürbüz B., Öztürk Y., Sezer M., Laguerre polynomial approach for solving linear delay difference equations. Applied Mathematics and Computation 2011 217 15 6765 6776 2-s2.0-79952361145 10.1016/j.amc.2011.01.112
19. Sezer M., Yalçinbaş S., Şahin N., Approximate solution of multi-pantograph equation with variable coefficients. Journal of Computational and Applied Mathematics 2008 214 2 406 416 2-s2.0-39049148015 10.1016/j.cam.2007.03.024 (Pubitemid 351241078)
20. Tohidi E., Legendre approximation for solving linear HPDEs and comparison with taylor and bernoulli matrix methods. Applied Mathematics 2012 3 410 416
21. Tohidi E., Bhrawy A. H., Erfani Kh., A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation. Applied Mathematical Modelling 2013 37 6 4283 4294 10.1016/j.apm.2012.09.032
22. Tohidi E., Bernoulli matrix approach for solving two dimensional linear hyperbolic partial differential equations with constant coefficients. American Journal of Computational and Applied Mathematics 2012 2 4 136 139 10.5923/j.ajcam.20120204.01
23. Toutounian F., Tohidi E., Shateyi S., A collocation method based on Bernoulli operational matrix for solving high order linear complex differential equations in a rectangular domain. Abstract, Applied, Analysis 2013 823098 10.1155/2013/823098
24. Yousefi S. A., Behroozifar M., Operational matrices of Bernstein polynomials and their applications. International Journal of Systems Science 2010 41 6 709 716 2-s2.0-77952938132 10.1080/00207720903154783
25. Yuzbasi S., Bessel polynomial solutions of linear differential, integral and integro-differential equations [M.S. thesis] 2009 Graduate School of Natural and Applied Sciences, Mugla University
26. Yuzbasi S., A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differen- tialdifference equations. Computers & Mathematics with Applications 2012 64 6 1691 1705 10.1016/j.camwa.2012.01.026
27. Yuzbasi S., Sezer M., An improved Bessel collocation method with a residual error function to solve a class of LaneEmden differential equations. Computer Modeling 2013 57 1298 1311
28. Yuzbasi S., Sezer M., Kemanci B., Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method. Applied Mathematical Modelling 2013 37 2086 2101
29. Saad Y., Iterative Methods for Sparse Linear Systems 2003 2nd Philadelphia, Pa, USA SIAM
30. Samadi O. R. N., Tohidi E., The spectral method for solving systems of Volterra integral equations. Journal of Applied Mathematics and Computing 2012 40 1-2 477 497 10.1007/s12190-012-0582-8
31. Tohidi E., Samadi O. R. N., Optimal control of nonlinear Volterra integral equations via Legendre polynomials. IMA Journal of Mathematical Control and Information 2013 30 1 67 83 10.1093/imamci/dns014