A Note on the Numerical Solution of High-Order Differential Equations

• Main Authors: WANG, Y., ZHAO, Yibao, WEI, G. W.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: High-order differential equation; Multi-boundary conditions; Local adaptive differential quadrature method; Physical Sciences and Mathematics
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/928; https://ink.library.smu.edu.sg/context/lkcsb_research/article/1927/viewcontent/Note_numerical_solution_HODE_pvoa.pdf
• Institution: Singapore Management University

Numerical solution of high-order differential equations with multi-boundary conditions is discussed in this paper. Motivated by the discrete singular convolution algorithm, the use of fictitious points as additional unknowns is proposed in the implementation of locally supported Lagrange polynomials. The proposed method can be regarded as a local adaptive differential quadrature method. Two examples, an eigenvalue problem and a boundary-value problem, which are governed by a sixth-order differential equation and an eighth-order differential equation, respectively, are employed to illustrate the proposed method.