The initial condition is the crucial starting point for any time-dependent simulation

The animation clearly highlights the crucial role of the Initial Condition (IC) in solving time-dependent partial differential equations like the diffusion equation. The IC sets the indispensable starting point for the simulation, defining the concentration $u_0$ everywhere in the domain at $t=$ 0 . The initial state, where high concentration is present across the domain, creates the potential energy-the concentration gradient-that then drives the entire process. The subsequent dynamic evolution, observed as the concentration profile flattens and decays over time, is the system moving away from this initial high-energy state toward a steady-state equilibrium, a process that is continuously constrained by the Boundary Conditions (BCs).

🎬Narrated Video

https://youtu.be/NdogRwZ0jSk

🏗️Structural clarification of Condensed Notes

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🗒️Downloadable Files - Recursive updates

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Copyright Notice

All content and images on this page are the property of Sayako Dean, unless otherwise stated. They are protected by United States and international copyright laws. Any unauthorized use, reproduction, or distribution is strictly prohibited. For permission requests, please contact [email protected]

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