×

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.

MSC:

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

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.