Numerical methods for solving differential equations
Numerical methods for solving differential equations are techniques used to approximate the solutions of differential equations (which describe various physical phenomena) when their analytical solutions are complex or do not exist. These methods involve various algorithms that allow for finding approximate solutions to ordinary differential equations (ODEs) and partial differential equations (PDEs). They typically perform discretization of the equations, meaning replacing the continuum with a finite number of points where the equation holds. Some of the most well-known methods include Runge-Kutta methods and linear multistep methods for solving ODEs with initial conditions, finite difference methods and collocation methods for solving ODEs with boundary conditions, as well as grid methods and finite element methods for solving PDEs.