International Journal of Mathematics and Computational Science

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Solution of Eighth Order Boundary Value Problem by Using Variational Iteration Method

Pages: 13-23 Views: 1520 Downloads: 343

[01]
Abdulla-Al-Mamun, Department of Mathematics, Islamic University, Kushtia, Bangladesh.
[02]
Mohammad Asaduzzaman, Department of Mathematics, Islamic University, Kushtia, Bangladesh.
[03]
Samsun Nahar Ananna, Department of Mathematics, Islamic University, Kushtia, Bangladesh.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the eighth order boundary value problems. It is to be mentioned that, presently, the literature on the numerical solutions of eighth order boundary value problem and associated eigen value problems is not available. By using a suitable transformation, the variational iteration method can be used to show that eighth order boundary value problems are equivalent to a system of integral equation. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with exact solution. Finally, we investigate the error between numerical solution and exact solution and draw the graph of error function by using Mathematica.

Variational Iteration Method, Boundary Value Problem, Mathematica, Exact Solution, Approximate Solution, Numerical Solution, Lagrange Multiplier, Absolute Error

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