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Legendre wavelet method for numerical solutions of partial differential equations
Author(s) -
Liu Nanshan,
Lin EnBing
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20417
Subject(s) - legendre polynomials , mathematics , legendre wavelet , convergence (economics) , partial derivative , square integrable function , partial differential equation , mathematical analysis , wavelet , associated legendre polynomials , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , wavelet transform , discrete wavelet transform , artificial intelligence , computer science , economics , economic growth
We introduce an orthogonal basis on the square [−1, 1] × [‐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. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010