The Galerkin Method is a numerical technique used to convert a continuous operator problem (like a differential equation) into a discrete problem, making it easier to solve using finite-dimensional spaces. This method involves choosing a set of basis functions and approximating the solution as a linear combination of these functions, while ensuring that the residual error is orthogonal to the span of the chosen basis. It connects to collocation methods as both aim to find approximate solutions, but the Galerkin approach focuses on minimizing the error in an integral sense.
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