Iterative method for solving linear operator equation of the first kind

In this work, we study the iterative method for solving linear operator equation of the first kind. We present a new version of method based on the applied the iterative performance on the modified Lavrentiev method. This method is used to resolve a linear operator problem of the first kind. The suggested iterative can used to compute approximate solutions with high quality than the (standard) modified Lavrentiev regularization method. We also compared the new iterative method (modified Lavrentiev) with Landweber iterative method. The numerical testing shows the efficiency of the new iterative method in its application to resolve the inverse heat equation when trying to find the boundary value function. • Studying of new iteration algorithm and mathematical experimentations show the efficiency of the new iteration method. • Iteration method is depended on decomposed the main linear operator by using polar decomposition in order to obtain unitary operator. • The new unitary operator increases the convergence of iteration

Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time

The boundary value problem, BVP, for the PDE heat equation is studied and explained in this article. The problem declaration comprises two intervals; the (0, T) is the first interval and labels the heating of the inside burning chamber, and the second (T, ∞) interval defines the normal cooling of the chamber wall when the chamber temperature concurs with the ambient temperature. It is necessary to prove the boundary function of this problem has its place in the space H10,∞ in order to successfully apply the Fourier transform method. The applicability of the Fourier transform for time to this problem is verified. The method of projection regularization is used to solve the inverse boundary value problem for the heat equation and to obtain an evaluation for the error between the approximate and the real solution. These results are new and of practical interest as shown in the numerical case study