In this paper, the inverse problems for the boundary value and initial value in a heat
equation are posed and solved. It is well known that those problems are ill posed. The …

The Landweber iteration method is one of the most popular methods for the solution of linear
discrete ill-posed problems. The diversity of physical problems and the diversity of operators …

Lavrent'ev regularization is one of the popular approaches to solving inverse ill-posed
problems. This article presents a new method by applying the iterative technique on the …

Particle size distribution is one of the important microphysical parameters to characterize the
aerosol properties. The aerosol optical depth is used as the function of wavelength to study …

To study the evolution law of axial force and shear stress of a full-length anchorage bolt in a
rectangular roadway during roadway driving and working face mining, based on the stress …

In this article the Tikhonov method used as a regularization technique for solving the inverse
problem liner operator equation of the first kind with noisy and noise-free data. We also …

Deep Learning (DL) algorithms have been used to model physical systems. However, the
success heavily relies on how DL methodologies accommodate the properties of a system …

We evaluate the first-order approximation solution piecewise by first-order polynomial
collocation with Quadrature scheme on second-type Fredholm integral equations. This …

We consider Fredholm integral equations of the first kind with symmetric kernels and use
Tikhonov's regularization property to transform them into second kind Fredholm equations …

This study is specially designed to solve the forward-backward heat equation in two
dimension to make use of thin plate splines and finite difference method. It should be noted …