首页 | 本学科首页   官方微博 | 高级检索  
     


Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients
Authors:Liu  Xiaojing  Zhou  Youhe  Wang  Jizeng
Affiliation:Key Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), the Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
Abstract:

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

Keywords:wavelet multiresolution interpolation  transcendental nonlinearity  localized steep gradient  singularly perturbed boundary value problem  Troesch's problem  
本文献已被 SpringerLink 等数据库收录!
点击此处可从《应用数学和力学(英文版)》浏览原始摘要信息
点击此处可从《应用数学和力学(英文版)》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号