An applicable approximation method and its application

In this work, by choosing an orthonormal basis for the Hilbert space L2[0,1], an approximation method for finding approximate solutions of the equation (I+K)x = y is proposed, called Haar wavelet approximation method (HWAM). To prove the applicability of the HWAM, a more general applicability theorem on an approximation method (AM) for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Furthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.