APPROXIMATE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF HIGHER-ORDER BY THE MODIFIED ADOMAIN DECOMPOSITION METHOD
DOI:
https://doi.org/10.53555/eijms.v6i1.46Keywords:
Boundary Value Problem, Adomain Decomposition Method, Boundary Conditions, Higher-Order non-linear ODE.”Abstract
This paper propose a new modified differential operator for solving third-order boundary value problems into higherorder ordinary differential equation. We found the differential operator for new two inverse operators which can be applied for solving equations at more than one type in different conditions. This paper is given five non-linear examples from a high-order, we got effective and easily approximate solutions to the exact solution.
References
. A.Boutayeb, and A.H.Twizell,“Finite-difference methods for the solution of special eight-order boundary value
problems,” Int. J. Com. Math., vol. 48, pp. 63-75, 1993.
. A.M.Wazwaz,“A new algorithm for calculating Adomian polynomials for nonlinear operators,” Appl. Math.
Comput., vol. 111, pp. 33-51, 2000.
. A.M.Wazwaz,“A new algorithm for solving boundary for higher-order integral differential equations,” Appl. Math.
Comp., vol. 118, pp. 327-342, 2001.
. A.M.Wazwaz,“A reliable algorithm for obtaining positive solutions for nonlinear boundary-value problems,”
Comput. Math. Appl., vol. 41, pp.1237-1246, 2001.
. A.M.Wazwaz,“Blow-up for solution of some linear wave equations with mixed nonlinear boundary conditions,”
Appl. Math. Comp., vol. 123, pp.133-140, 2001.
. A.M.Wazwaz,“The modified Adomian decomposition method for solving linear and nonlinear boundary-value
problems of tenth-order and 12thorder,” Int. J. Nonlinear Sci. Numr. Simul, vol. 1, pp. 17-24, 2000.
. A.M.Wazwaz,“The numerical solution of fifth-order BVP by the decomposition method,” J. Comput. Appl. Math.,
vol. 136, pp.259-270, 2001.
. E.Deeba, S.Khuri and S.Xie,“An algorithm for solving boundary value problems,” J. Comp. Phy. vol. 159, pp. 125-
, 2000.
. G.Adomian, and R.Rach,“Analytic solution of nonlinear boundary value problems in severl dimensions,” Math.
Anal. Appl. vol. 174, pp. 118-127, 1993.
. G.Adomian,“Nonlinear stochastic operator equations,” Acadmic Press, SanDiego, CA, 1986.
. G.Adomian,“Solving frontier problems of physics: the decomposition method,” Kluwer academic publishers
London, 1994.
. KNS.Viswanadham, and Y.Showri Raju,“Quintic B-spline Collocation Method for Eighth Order Boundary Value
Problems,” Advances in Computational Mathematics and its Applications, vol. 1, pp. 47-52, 2012.
. R.P.Agarwal,“Boundary value problems for high-order differential equations,” World Scientific, Singapore, 1986.
. S.Chandrasekhar,“Hydrodynamic and Hydromagnetic Stability,”Dover, New york,NY, 1981.
. Y.Q.Hasan,“Modified Adomian decomposition method for second order singular initial value problems,” Advances
in Computational Mathematics and its Applications., vol. 1, pp. 94-99, 2012
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