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Generalized Gaussian integral method for calculations of scaling function transform of wavelets and its applications. (Chinese. English summary) Zbl 0941.65015

This paper discusses the generalized Gaussian quadrature with weights being Daubechies scaling functions. In some cases of algebraic accuracy 3, the coefficients and knots are obtained approximately by numerical computation. The composite generalized Gaussian quadrature is established by dividing uniformly the interval into \(2^m\) subintervals and then applying the Gaussian quadrature in each interval. It is shown that the composite generalized Gaussian integral method converges as \(m\to\infty\). The method is illustrated by an example of two-point boundary value problem with strong nonlinearity.

MSC:

65D32 Numerical quadrature and cubature formulas
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
41A55 Approximate quadratures
65T60 Numerical methods for wavelets
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