Galerkin method with new quadratic spline wavelets for integral and integro-differential equations
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Date
2019-10-18
Authors
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Volume Title
Publisher
ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS
Abstract
The paper is concerned with the wavelet-Galerkin method for the numerical solution of Fredholm linear integral equations and second-order integro-differential equations. We propose a construction of a quadratic spline-wavelet basis on the unit interval, such that the wavelets have three vanishing moments and the shortest support among such wavelets. We prove that this basis is a Riesz basis in the space L-2(0, 1). We adapt the basis to homogeneous Dirichlet boundary conditions, and using a tensor product we construct a wavelet basis on the hyperrectangle. We use the wavelet-Galerkin method with the constructed bases for solving integral and integro-differential equations, and we show that the matrices arising from discretization have uniformly bounded condition numbers and that they can be approximated by sparse matrices. We present numerical examples and compare the results with the Galerkin method using other quadratic spline wavelet bases and other methods.
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Subject(s)
Wavelet, Quadratic spline, Short support, Galerkin method, Integral equation, Integro-differential equation