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Corresponding Author

Dina Reda

Subject Area

Mathematics and Engineering Physics

Article Type

Original Study

Abstract

In the following work, the numerical investigation of biharmonic equation is explored. The approximate solution is approximated at specific points in the solution domain by using the collocation method based on the modified bi-quintic b-spline basis functions. These modified basis functions vanish at the boundary points. The main properties of these basis functions are discussed in detail. The method is based on reducing the proposed problem to a linear system of equations. The boundary conditions are combined in the resulting linear system of equations in specific order to guarantee that the approximate solution coincides with the exact solution at the boundary points. Three numerical examples show the effectiveness of our method, and the accuracy is measured by comparing three different types of error between approximate and exact solutions. The outcomes are graphically depicted to assess the performance of the intended method. The proposed method is easy to implement, and numerical results ensure that the method approximates the solution of the biharmonic problem very well.

Keywords

Modified Quintic B-spline, Biharmonic equations, Dirichlet problem, Collocation method

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