Galerkin method

The Galerkin method is a mathematical technique used to find approximate solutions to complex problems, often in engineering and physics. It works by transforming a difficult equation into a simpler one. Instead of solving the original problem directly, it uses a set of trial functions (simple, manageable shapes) to represent the solution. By ensuring that the residual error (the difference between the real problem and the approximation) is minimized in a weighted sense, this method yields effective approximations that are easier to calculate, while maintaining accuracy to the original problem's behavior.