Parabolic partial differential equations (PDEs) play a pivotal role in modelling processes that involve diffusion and thermal dynamics. Over recent decades, the study of their controllability – the ...

Convergence of a subsequence of approximate solutions arising from a full discretization is shown for a general class of quasi-linear parabolic problems. The numerical method combines the backward ...

Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear ...

Off-axis paraboloid reflector is a special optical element, its main function is to focus the incident light to a certain distance from the optical axis. The working principle is based on the ...