A note on the numerical solution of high-order differential equations

  • Authors:

  • Y. Wang;Y. B. Zhao;G. W. Wei

  • Affiliations:

  • Department of Computational Science, National University of Singapore, Singapore 117543, Singapore;Department of Computational Science, National University of Singapore, Singapore 117543, Singapore;Department of Computational Science, National University of Singapore, Singapore 117543, Singapore and Department of Mathematics, Michigan State University, East Lansin, MI

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2003

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Abstract

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.