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Solution of boundary value problems for integro-differential equations by using differential transform method. (English) Zbl 1090.65145
{\it J. K. Zhou} introduced what some authors call the differential transform method (DTM) cf. Differential transformations and its application for electrical circuits (Chinese), Huazhong University Press, Wuhan, China (1986)]. The idea behind this notion is to assume analyticity and to use Taylor series expansion to determine the solution. The author states several properties of the DTM transformation in the one-dimensional case, i.e., properties of Taylor coefficients, in a purely formal way. Similar statements can be found in the two-dimensional setting [cf. {\it F. Ayaz}, Appl. Math. Comput. 147, No. 2, 547--567 (2004; Zbl 1032.35011), {\it C. K. Chen} and {\it S. H. Ho}, Appl. Math. Comput. 106, No. 2--3, 171--179 (1999; Zbl 1028.35008)]. Three examples are calculated at the end of the paper.

65R20Integral equations (numerical methods)
45J05Integro-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] Rashed, M. T.: Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations. Appl. math. Comput. (2003) · Zbl 1048.65133
[3] 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
[4] 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
[5] Maleknejad, K.; Mahmoudi, Y.: Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations. Appl. math. Comput. 145, 641-653 (2003) · Zbl 1032.65144
[6] Maleknejad, K.; Mirzaee, F.; Abbasbandy, S.: Solving linear integro-differential equations system by using rationalized Haar functions method. Appl. math. Comput. (2003) · Zbl 1056.65144
[7] Zhou, J. K.: Differential transformation and its application for electrical circuits. (1986)
[8] Wazwaz, A. -M.: A reliable algorithm for solving boundary value problems for higher-order integro-differential equations. Appl. math. Comput. 118, 327-342 (2001) · Zbl 1023.65150