Solution of Hallenʹs integral equation using multiwavelets Original Research Article

An effective method based upon Alpert multiwavelets is proposed for the solution of Hallenʹs integral equation. The properties of Alpert multiwavelets are first given. These wavelets are utilized to reduce the solution of Hallenʹs integral equation to the solution of sparse algebraic equations. In order to save memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of resulted matrix equation.