Derive the finite difference scheme for the numerical solution of the first-order diffusion equation IBVP using the Crank-Nicolson method

In the article, a differential scheme is created for first-order diffusion equation using Crank-Nicolson method. The stability of was checked Neumann To solve problem numerically, intervals were found Neman This work presents an analysis two-dimensional Von analysis. widely used numerical method solving partial equations that combines explicit and implicit schemes. important factor to consider when choosing equations, as instability can cause inaccurate solutions. We show unconditionally stable, meaning it be wide range parameters without being affected by instability. Overall, implementation presented in this provide framework designing analyzing methods scheme. crucial ensuring accuracy reliability solutions equations.