Legendre wavelet method for numerical solutions of partial differential equations

Nanshan Liu, En Bing Lin

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

We introduce an orthogonal basis on the square [-1,1] x [-1,1] generated by Legendre polynomials on [-1,1], and define an associated expression for the expansion of a Riemann integrable function. We describe some properties and derive a uniform convergence theorem. We then present several, numerical experiments that indicate that our methods are more efficient and have better convergence results than some other methods.

Original languageEnglish
Pages (from-to)81-94
Number of pages14
JournalNumerical Methods for Partial Differential Equations
Volume26
Issue number1
DOIs
StatePublished - Jan 2010

Keywords

  • Associated expansions
  • Error estimate of numerical solutions
  • Legendre polynomial
  • Orthogonal basis

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