Solve the differential equation in problem 8 for the following boundary conditions using the Galerkin method: Assume

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Solve the differential equation in problem 8 for the following boundary conditions using the Galerkin method:

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Assume the approximate solution as:

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where \(\phi_{0}(x)\) is a function that satisfies the essential boundary conditions, and \(\phi_{1}(x)\) is the weight function that satisfies the homogeneous part of the essential boundary conditions, that is, \(\phi_{1}(0)=\phi_{1}(1)=0\). Hence, assume the functions as follows:

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Compare the approximate solution with the exact solution by plotting their graphs. The exact solution can be derived as:

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Data From Problem 8:

Consider the following differential equation:

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Related Book For  book-img-for-question

Introduction To Finite Element Analysis And Design

ISBN: 9781119078722

2nd Edition

Authors: Nam H. Kim, Bhavani V. Sankar, Ashok V. Kumar

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