Wavelets in Boundary Value Problems
Jaideva C. Goswami, Andrew K. Chan · 2010
In boundary value problems (BVPs) functions are not known explicitly; some of their properties along with function values are known at a set of certain points in the domain of interest. In this chapter we discuss the applications of wavelets in solving such problems. It deals with the linear operators. The linear operator equation is converted to a system of linear equations with the help of a set of complete bases, which is then solved for the unknown coefficients. Method of moments is probably the most widely used technique for solving integral equations in electromagnetics. The chapter briefly describes the applications of wavelets in partial differential equations (PDEs), particularly the multiresolution time domain (MRTD) method, and provide references. It present some numerical examples for the scattering problems. Both semiorthogonal and orthogonal wavelets have been used for solving integral equations. Controlled Vocabulary Terms boundary-value problems; wavelet transforms