ABSTRACT
This chapter summarizes the idea of integral transforms versus eigenfunction expansion. It deals with problems that need to be modeled by integral equations and integro-differential equations and discusses the basics of integral transform and its introduction is primarily for setting the scene for the more difficult problems of integral equations and of integro-differential equations. A number of more notable integro-differential equations are reported. Integro-differential equations may also appear in a pair of coupled systems. The chapter reviews the concept of the integral transform, including the Laplace transform, Fourier transform, Hankel transform, Mellin transform, and Hilbert transform. Nonlinear Volterra integro-differential equations are solved using the Adomian decomposition technique, whereas nonlinear Fredholm integro-differential equations are solved by using the direct computation method for the case of separable kernels.
