A method for the numerical solution of the integro-differential equations. (English) Zbl 1121.65127

The authors propose a method for the numerical solution of Fredholm-type integro-differential equations. The method is based on a subdivision of the interval of interest, combined with a Taylor series expansion. Some numerical examples are given, but a theoretical analysis has not been done.


65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
Full Text: DOI


[1] Avudainayagam, A.; Vani, C., Wavelet-Galerkin method for integro-differential equations, Appl. Numer. Math., 32, 247-254 (2000) · Zbl 0955.65100
[2] Chen, C. K.; Ho, S. H., Solving partial differential equations by two-dimensional differential transform method, Appl. Math. Comput., 106, 171-179 (1999) · Zbl 1028.35008
[3] Abdel-Halim Hassan, I. H., Differential transformation technique for solving higher-order initial value problems, Appl. Math. Comput., 154, 299-311 (2004) · Zbl 1054.65069
[4] Jang, M. J.; Chen, C. L.; Liy, Y. C., On solving the initial-value problems using the differential transformation method, Appl. Math. Comput., 115, 145-160 (2000) · Zbl 1023.65065
[5] Jang, M. J.; Chen, C. L.; Liu, Y. C., Two-dimensional differential transform for partial differential equations, Appl. Math. Comput., 121, 261-270 (2001) · Zbl 1024.65093
[6] Sezer, M., Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol., 5, 625-633 (1994) · Zbl 0823.45005
[7] Sezer, M., A method for the approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Educ. Sci. Technol., 6, 821-834 (1996) · Zbl 0887.65084
[8] Rashed, M. T., Lagrange interpolation to comput the numerical solutions differential and integro-differential equations, Appl. Math. Comput. (2003) · Zbl 1025.65063
[9] Kanwal, R. P.; Liu, K. C., A Taylor expansion approach for solving integral equations, Int. J. Math. Educ. Sci. Technol., 3, 411-414 (1989) · Zbl 0683.45001
[10] El-Sayed, S. M.; Abdel-Aziz, M. R., A comparison of adomian’s decomposition method and Wavelet-Galerkin method for solving integro-differential equations, Appl. Math. Comput., 136, 151-159 (2003) · Zbl 1023.65149
[11] Hosseini, S. M.; Shahmorad, S., Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases, Appl. Math. Model., 27, 145-154 (2003) · Zbl 1047.65114
[12] Yalcinbas, S., Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 127, 195-206 (2002) · Zbl 1025.45003
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