井冈山大学学报（自然科学版）2026，Vol.47Issue(5)：12-20,9.DOI:10.3969/j.issn.1674-8085.2026.05.002
基于3-尺度Legendre小波的微分方程特征值问题数值解
Numerical solution of eigenvalue problems for differential equation based on scale-3 Legendre wavelets
摘要
Abstract
A numerical method for solving eigenvalue problems of higher-order differential equations based on scale-3 Legendre wavelets is proposed.The wavelet basis functions are constructed by normalizing Legendre polynomials,and the uniform convergence of their expansion approximation for the unknown functions is proven.The Riemann-Liouville fractional integral formula is derived via the Laplace transform.Fourth-order and sixth-order differential equation eigenvalue problems are taken as numerical examples and compared with the Haar wavelet method for validation.The results show that the scale-3 Legendre wavelet method achieves higher accuracy in eigenvalues with fewer collocation points,and the numerical results using Gauss points as collocation points are superior to those using Newton-Cotes points.关键词
微分方程特征值问题/3-尺度Legendre小波/Gauss配置点/Haar小波/Riemann-Liouville分数阶积分Key words
eigenvalue problems of differential equations/scale-3 Legendre wavelets/Gauss point/Haar wavelets/Riemann-Liouville fractional integral分类
数理科学引用本文复制引用
秦玺鹏,许小勇,汤思颖..基于3-尺度Legendre小波的微分方程特征值问题数值解[J].井冈山大学学报（自然科学版）,2026,47(5):12-20,9.基金项目
江西省自然科学基金项目(2020BABL201006) （2020BABL201006）
