☁️Delving into the World of Partial Differential Equations

Partial Differential Equations (PDEs) are a fundamental mathematical language that describes how quantities change across space and time, serving as essential models for phenomena in the natural world and engineered systems, with key examples including the Wave, Heat, Transport, Schrödinger, and Elastic Membrane equations, each characterized by distinct mathematical properties (elliptic, hyperbolic, or parabolic).

This "Cloud computing" section explores Partial Differential Equations (PDEs), specifically demonstrating the Wave Equation using a 1D finite difference method, the Heat Equation with a 1D explicit finite difference scheme, and the Transport Equation via a 1D upwind scheme.

🎬Animated result

the Wave Equation (1D example using finite difference)

the Heat Equation (1D example using explicit finite difference)

the propagation of a wave on a 2D plane