C-N Method for Solving Partial Differential Equations

This program implements the Crank-Nicolson (C-N) method for solving parabolic partial differential equations with fixed spatial step size, specifically addressing equations of the form: du/dx - a * d²u/dx² = 0. The implementation features adjustable diffusion coefficient 'a', allowing users to modify this parameter directly in the code for solutions with different constant coefficients. Through iterative updates within the main computational loop, the program can also handle variable coefficient scenarios. The numerical scheme utilizes a finite difference discretization where the C-N method provides unconditional stability while maintaining second-order accuracy. Key components include matrix assembly for the implicit solver and boundary condition handling. Detailed documentation is available in the compressed package, and the modular code structure permits customization and extension according to specific requirements. This implementation offers an efficient and reliable approach for solving PDE problems, with broad applications in academic research and engineering practice. The code structure facilitates easy integration of different initial conditions and boundary treatments while maintaining numerical stability through the implicit time-marching scheme.