Trigonometric wavelet method for some elliptic boundary value problems

Abstract

In this paper, we apply trigonometric wavelet method to investigate the numerical solution of elliptic boundary value problem in an exterior unit disk. The simple computation formulae of the entries in the stiffness matrix are obtained. It shows that we only need to compute 2(2 j + 1) elements of one 2 j+2 × 2 j+2 stiffness matrix. Moreover, the error estimates of the approximation solutions are given and some test examples are presented.

Numerical solution ofnth-order integro-differential equations using trigonometric wavelets

“…Lemma 7 (Quak [24] and Shan and Du [25]) For any J ∈ N 0 , the interpolation operator P J maps any real-valued differentiable 2 -periodic function f into the space V J that is defined as follows:…”

“…denote the inner product in L 2 2 , and T m denote the linear space of trigonometric polynomials with degree not exceeding m. For all m ∈ N, the Dirichlet kernel D m (x) and its conjugate kernelD m (x) are defined as [24,25] …”

Numerical solution of hypersingular equation using recursive wavelet on invariant set

“…The wavelet-based Galerkin method has also been developed to solve the natural boundary integral equation [14][15][16]. A number of different schemes have been suggested to adapt the notion of multiresolution analysis which was originally introduced for L 2 (R) to space on a bounded interval, say L 2 [0, 1] [17].…”