Tchebychev Multi-wavelet Basis for Solving Boundary Integral Equation

In this paper, using orthogonality of Tchebychev polynomials, we present anorthonormal wavelet basis for L2[0, 1]. We use this basis for solving Neumannproblems with Galerkin method. The property of this basis is that a variety ofintegral operators is represented in this basis as sparse matrices, to high precision.Some examples are solved to illustrate the efficiency and accuracy of this method.