Legendre Wavelet Method for a Class of Fourth-Order Boundary Value Problems

Iranian Journal of Optimization

دوره 12، شماره 2، اسفند 2020، صفحه 259-276   

نوع مقاله: Research Paper

نویسندگان

Sarkout Abdi¹؛ Aram Azizi^{* 2}؛ Mahmoud Shafiee³؛ Jamshid Saeidian⁴

¹Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

²1. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran 2. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran

³Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

⁴1.Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran 2. Faculty of Mathematical, Sciences and Computer, Kharazmi University, 50 Taleghani Avenue, Tehran,1561836314, Iran

چکیده

In this paper we apply an approximate method based on Galerkin approach with Legendre wavelets basis, on a class of fourth order boundary value problems. The approach reduces the main equation to a system of linear algebraic equations that could be solved numerically. The operational matrix of the method is obtained, and the convergence of the method is proved. we approximate the solution and its higher order derivatives, for some special examples and compare the results with some other numerical methods. The results show the effectiveness of the proposed method.

کلیدواژه‌ها

Legendre wavelet method؛ Operational matrix؛ Boundary value problems