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A reliable algorithm for solving boundary value problems for higher-order integro-differentiable equations. (English) Zbl 1023.65150
Summary: The aim of this paper is to present an efficient analytical and numerical procedure for solving boundary value problems for higher-order integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. The analysis is accompanied by numerical examples. The results demonstrate reliability and efficiency of the proposed algorithm.

65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
45J05Integro-ordinary differential equations
Full Text: DOI
[1] Agarwal, R. P.: Boundary value problems for high ordinary differential equations. (1986) · Zbl 0619.34019
[2] Morchalo, J.: On two point boundary value problem for integro-differential equation of second order. Fasc. math. 9, 51-56 (1975) · Zbl 0363.45005
[3] Morchalo, J.: On two point boundary value problem for integro-differential equation of higher order. Fasc. math. 9, 77-96 (1975) · Zbl 0363.45006
[4] Agarwal, R. P.: Boundary value problems for higher order integro-differential equations nonlinear analysis. Theory, meth. Appl. 7, No. 3, 259-270 (1983) · Zbl 0505.45002
[5] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[6] Adomian, G.: A review of the decomposition method in applied mathematics. J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053
[7] A.M. Wazwaz, A First Course in Integral Equations, World Scientific, River Edge, NJ, 1997 · Zbl 0924.45001
[8] Wazwaz, A. M.: Analytical approximations and Padé approximants for Volterra’s population model. Appl. math. Comput. 100, 13-25 (1999) · Zbl 0953.92026
[9] Wazwaz, A. M.: A reliable modification of Adomian’s decomposition method. Appl. math. Comput. 92, 1-7 (1998)
[10] Wazwaz, A. M.: A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. math. Comput. 111, 33-51 (2000) · Zbl 1023.65108
[11] Abu-Sitta, A. M. M.: A note on a certain boundary-layer equation. Appl. math. Comput. 4, 73-77 (1994) · Zbl 0811.34013
[12] Weyl, H.: On the differential equations of the simplest boundary layer problems. Ann. math. 43, No. 2, 381-407 (1942) · Zbl 0061.18002
[13] Wazwaz, A. M.: A study on a boundary-layer equation arising in an incompressible fluid. Appl. math. Comput. 87, 199-204 (1997) · Zbl 0904.76067
[14] Boyd, J.: Padé approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Comput. math. 11, No. 3, 299-313 (1997)
[15] Wazwaz, A. M.: The modified decomposition method and Padé approximants for solving Thomas--Fermi equation. Appl. math. Comput. 105, No. 1, 11-19 (1999) · Zbl 0956.65064
[16] Baker, G. A.; Gravis-Morris, P.: Essentials of Padé approximants. (1996)