Abstract
We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions. These results have been compared with the results that are obtained by variational iteration method (VIM), homotopy perturbation method (HPM), Adomian decomposition method (ADM), variation of parameters method (VPM), and homotopy analysis method (HAM). Obtained results show that our method is very effective.
Highlights
Consider the seventh-order boundary value problem [1,2,3,4,5]: u(7) (x) = N (x, u (x)), 0 ≤ x ≤ 1, (1)with boundary conditions u(i) (0) = Ai, i = 0, 1, 2, 3, (2)u(j) (1) = Bj, j = 0, 1, 2.The analytical solution of seventh-order differential equations are rarely exists in literature
We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions
We introduced an algorithm for solving the seventh-order problem with boundary conditions
Summary
Consider the seventh-order boundary value problem [1,2,3,4,5]: u(7) (x) = N (x, u (x)) , 0 ≤ x ≤ 1, (1). The aim of this work is to apply reproducing kernel Hilbert space method (RKHSM) [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] to solve the seventh-order boundary value problems. Numerical results of the seventh-order boundary value problems have been obtained by this method in our work. This study shows that the proposed method can be considered as an alternative technique for solving linear and nonlinear problems in science and engineering [29,30,31]
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