Sumudu Applications to Maxwell's Equations

Abstract

A main attribute of the Sumudu transform lies in its units preserving property. Connected to Fourier, bilateral, two-sided, and ordinary Laplace transforms, the Sumudu is beginning to claim more fame through its unique advantages and pragmatic applications. Here, Maxwell's equations, pertaining to transient electromagnetic planar, (TEMP), waves propagation in lossy media, are shown to yield electric fleld solutions, through Sumudu transformation. 1. A HANDFUL OF INTEGRAL TRANSFORMS The Laplace transform usage dates back to Euler's 1737 'De Constructione Aequationum'. Its use has been prevalent in solving ordinary difierential, difierence, and functional equations. Like Euler, a list of contributors to the Laplace transform theory, many of whom have other transforms attached to their names, include but is certainly not limited to Lagrange, Laplace, Fourier, Poisson, Cauchy, Abel, Liouville, Boole, Riemann, Pincherle, Amaldi, Tricomi, Picard, Mellin, Borel, Heaviside, Bateman, Titchmarsh, Bernstein, Doetsch, and Widder (1). The bilateral Laplace transform is an integral transform closely related to the Fourier transform, the ordinary one-sided, and the two- sided or s-multiplied Laplace transform (5,12). For, f(t), a real or complex valued function of the real variable t taking domain over all real numbers, the bilateral Laplace transform is deflned by the integral, B(f(t))(s) = F(s) = Z +1 i1 f(t)e ist dt: (1) Albeit less famed than its one sided counterpart, the bilateral transform can be encountered in all areas of scientiflc applications where the functions used may be deflned, but not necessarily, over subsets of both sides of the real axis. For instance, the moment generating function of a continuous probability density function, p(x), is deflned, B(p(x))(is). Given any real number, a, and the shifted unit step function, Ha(t), of the Heaviside function, H(t) = H0(t),