Abstract
In this paper, we use the modified decomposition method for solving the system of third-order nonlinear boundary value problems associated with obstacle problems. Some examples of system of third-order nonlinear boundary value problems are given. The comparison of the results obtained by modified decomposition method with modified variation of parameters method is also given. Results are also shown graphically that demonstrate the nature of the obstacles in particular problems. The results are very encouraging indicating the reliability and efficiency of the technique.
Highlights
Several techniques have been used to solve system of linear thirdorder boundary value problems associated with obstacle, contact and unilateral problems
Adomian [12] developed a novel technique known as Adomian decomposition method for solving boundary value problems
The comparison of the results obtained by this method are given with modified variation of parameters method
Summary
Much attention has been given to solve a system of third-order obstacle boundary value problems, see [1,2,3,4, 5, 6, 7]. We consider the following systems of third-order nonlinear boundary value problems:. Several techniques have been used to solve system of linear thirdorder boundary value problems associated with obstacle, contact and unilateral problems. All the above mentioned methods are proposed to solve linear system of boundary value problems associated with obstacle, contact and unilateral problems. Noor et al [5] have proposed modified variation of parameters method for solving system of nonlinear obstacle boundary value problems of even and odd orders. Adomian [12] developed a novel technique known as Adomian decomposition method for solving boundary value problems. We again use the modified decomposition method to solve systems of thirdorder nonlinear obstacle boundary value problems. We implement this technique for solving systems of third-order nonlinear boundary value problems. The idea and technique of this paper may lead to novel applications of these problems in pure and applied sciences
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