Solving Heat diffusion differential equation using MATLAB

Introduction

MATLABSolutions demonstrate In this particular task, our objective is to adeptly execute a numerical methodology for effectively tackling the Heat diffusion equation. We shall be employing the center finite difference approach, and with unwavering precision, we will explore both the explicit and implicit Euler methods. The Heat diffusion equation as our guiding principle, encapsulating the intricate interplay of thermal dynamics.

Solving the heat diffusion equation in MATLAB typically involves using numerical methods, such as finite differences or finite element methods. Here, I'll provide a basic example of how to solve the 1D heat diffusion equation using the finite difference method in MATLAB. You can extend this to 2D or 3D problems as needed.

• $u$ is the temperature distribution as a function of time ($t$) and space ($x$).
• $\alpha$ is the thermal diffusivity.

Here's a step-by-step guide on how to solve this equation in MATLAB:

Step 1: Define the Problem
Before you start coding, you need to define the problem's parameters, such as the initial temperature distribution, boundary conditions, thermal diffusivity, spatial and temporal discretization, and simulation time.

Step 2: Discretize Space and Time
In MATLAB, you'll need to discretize the spatial and temporal domains. This involves creating a grid for $x$ and $t$. You can use the linspace function for spatial discretization and specify a time step size for temporal discretization.