when using the KAN network to solve the 2D heat conduction problem, the results near the heat source do not match those from the finite difference method. how to solve it?

Abstract: The current paper presents a numerical technique in solving the 3D heat conduction equation. The Finite Volume method is used in the discretisation scheme. Gauss's theorem has also been ...

Solving and visualizing the 2D heat conduction equation over a simple 2D rod being heated from both its ends. The solution is the temperature field you'd observe over the geometry of the rod at ...

In this paper, the method for constructing exact solutions of unsteady heat conduction problem for areas, which are made of rectangles, is proposed. The analysis of the results of computational ...

Abstract The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An ...

Eq7 Conclusion While this article presents the basics of numerical methods for solving the 2D heat transfer equation, there are several other factors to consider when solving engineering problems ...

2 Department of Mathematics, Air University, Islamabad, Pakistan This study reveals the extension of a mathematical model of heat and mass transfer of fluid flow over a sheet by incorporating the ...

The current paper presents a numerical technique in solving the 3D heat conduction equation. The Finite Volume method is used in the discretisation scheme. Gauss's theorem has also been employed for ...