A higher-order collocation technique based on Haar wavelets for fourth-order nonlinear differential equations having nonlocal integral conditions

被引:4
作者
Ahsan, Muhammad [1 ,2 ]
Lei, Weidong [1 ]
Khan, Amir Ali [2 ]
Ahmed, Masood
Alwuthaynani, Maher [3 ]
Amjad, Ayesha [4 ,5 ]
机构
[1] Harbin Inst Technol, Sch Civil & Environm Engn, Shenzhen 518055, Peoples R China
[2] Univ Swabi, Dept Math, Swabi, Pakistan
[3] Coll Khurma Univ Coll, Taif Univ, Dept Math, POB 11099, Taif 21944, Saudi Arabia
[4] Silesian Tech Univ, Fac Org & Management, PL-44100 Gliwice, Poland
[5] Univ Coimbra, Ctr Mech Engn Mat & Proc CEMMPRE, Polo 2, P-3030788 Coimbra, Portugal
关键词
Nonlinear differential equation; Haar wavelet; Collocation method; Quasi-linearization approach; NUMERICAL-SOLUTION; SIMULATION; ALGORITHM;
D O I
10.1016/j.aej.2023.11.066
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This article encounters the use of two wavelet methods, namely the collocation method based on Haar wavelets (CMHW) and the higher-order collocation method based on Haar wavelets (HCMHW), to solve linear and nonlinear fourth-order differential equations with different forms of given data such as two-point boundary conditions and two-point integral boundary conditions. Managing these types of boundary conditions can be challenging in numerical methods. However, in this study, these types of equations are handled in a simple manner using the Haar wavelet expressions, as provided in the given information. In the case of nonlinear problems, the quasi-linearization technique is introduced to linearize the equation. Nonlinear fourth-order differential equations are transformed into a simple linear system of algebraic equations using the quasi-linearization technique and Haar wavelets. These equations are then solved very easily to find the solution of the differential equations. The convergence rate and stability of both the methods are studied in details. The convergence rate of the proposed HCMHW is faster than the CMHW (2+2s>2,s=1,2 & mldr;). Some of the examples are given to indicate the better performance and accuracy of the proposed HCMHW.
引用
收藏
页码:230 / 242
页数:13
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