Haar Wavelet Method for Solving High-Order Differential Equations with Multi-Point Boundary Conditions

Document Type : Research Paper


1 Department of Mathematics, Yazd University, Yazd, Iran

2 Laboratory for Intelligent Computing and Financial Technology, Department of Mathematical Science, Xi’an Jiaotong-Liverpool University, Suzhou 215123, Jiangsu, China

3 University of Applied Science and Technology (UAST), Ghand Center, Karaj, Iran


In This paper, the developed Haar wavelet method for solving boundary value problems is described. As known, the orthogonal Haar basis functions are applied widely for solving initial value problems, but In this study, the method for solving systems of ODEs associated with multipoint boundary conditions is generalized in separated or non-separated forms. In this technique, a system of high-order boundary value problems of ordinary differential equations is reduced to a system of algebraic equations. The experimental results confirm the computational efficiency and simplicity of the proposed method. Also, the implementation of the method for solving the systems arising in the real world for phenomena in fluid mechanics and construction engineering approves the applicability of the approach for a variety of problems.


Main Subjects

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