On Solutions of Boundary Value Problem for Fourth-Order Beam Equations
In this paper, we consider the fourth-order linear differential equation u(4) +f(x)u = g(x) subject to the mixed boundary conditions u(0) = u(1) = u‘‘(0) = u‘‘(1) = 0. We first establish sufficient conditions on f(x) that guarantee a unique solution of this problem in the Hilbert space by using an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2016-05-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/815 |
| Summary: | In this paper, we consider the fourth-order linear differential equation u(4) +f(x)u = g(x) subject to the mixed boundary conditions u(0) = u(1) = u‘‘(0) = u‘‘(1) = 0. We first establish sufficient conditions on f(x) that guarantee a unique solution of this problem in the Hilbert space by using an a priori estimate. Accurate analytic solutions in series forms are obtained by a new variation of the Duan-Rach modified Adomian decomposition method (DRMA), and then extend this approach to some boundary value problems of fourth-order nonlinear beam equations. Also, a comparison of the two approximate solutions by the ADM with the Green function approach is presented.
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| ISSN: | 1392-6292 1648-3510 |