The heat conduction equation (also called the diffusion equation) describes how temperature spreads through a medium over time.
The wave equation describes propagation of disturbances (vibrations, sound, light, water waves) through a medium at a finite speed.
Elliptic equations describe steady-state (time-independent) equilibrium configurations — not evolution over time. The classic example is Laplace's/Poisson's equation.
Main Solution Methods
Separation of variables assumes u(x,t) = X(x)T(t)
Method of characteristics or first-order equations
Integral transforms Fourier, Laplace
Green's functions
Numerical methods - finite differences, finite elements (for cases without closed-form solutions)
The application applies numerical methods for heat,wave and elliptic equations And changes parameters in dialog. Results shows graphically and in parameters.