A numerical technique for gradient-type interface in the inverse scattering problems is presented in this paper. Such an interface is a point at which the velocity profile suffers a jump in first derivative. The time domain approach to scattering from gradient-type interface leads to an integro-differential equation. Using Legendre-Gauss-Lobatto nodes we construct the Nth polynomial interpolation to solve the integro-differential equation. An illustrative example is included to demonstrate the accuracy of the proposed method.
The properties of the hybrid functions which consists of block-pulse functions plus Chebyshev polynomials are presented. By using these hybrid functions, the differential and integral expressions which arise in the radiative transfer equation are converted into some linear systems of differential equations which can be solved for the unknown coefficient. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results.