☁️Navigating the Landscape of Numerical Methods for PDEs

Since analytical solutions for Partial Differential Equations (PDEs) are often impossible, numerical methods like the Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM) provide powerful approximation tools, each employing distinct approaches (discretizing derivatives, variational formulation, and integral conservation laws, respectively) and relying on concepts like stability analysis and boundary conditions to solve diverse problems across various fields.

This section on "Navigating the Landscape of Numerical Methods for PDEs" within cloud computing focuses on applying and simplifying Finite Element Method (FEM) and Finite Volume Method (FVM) to one-dimensional problems like the heat equation and steady-state transport, exemplified by heat diffusion along a rod.

🎬Animated result

The diffusion of heat along a 1D rod over time