DOI: https://doi.org/10.36719/2663-4619/117/151-155
Shahnaz Qadimova
Azerbaijan State Oil and Industry University
master student
https://orcid.org/0009-0008-4399-6967
kadimovashahnaz01@gmail.com
The Finite Difference Method for Solving Boundary Value
Problems of Parabolic Equations
Abstract
The finite difference method is one of the widely applied numerical techniques for solving parabolic equations. In this approach, differential equations are discretized and transformed into finite difference equations. Explicit, implicit, and Crank-Nicholson schemes exhibit different stability and convergence properties. During the computation process, the Courant-Friedrichs-Lewy (CFL) condition is a key factor in ensuring stability. If the time and spatial steps are not chosen correctly, the solution may become unstable. This method is effectively used in mathematical models of heat conduction, diffusion, and other physical processes.
Keywords: finite difference method, differential equations, explicit and implicit schemes, convergence, stability, Courant-Friedrichs-Lewy (CFL) condition