Variational formulation

The variational formulation is a method used in mathematics and physics to find solutions to complex problems, especially involving waves, structures, or fields. Instead of directly solving the equations, it involves expressing the problem as an optimization task—searching for the best possible state or function that minimizes or maximizes a certain quantity, called a functional. Think of it like finding the most efficient shape or configuration that achieves a desired outcome. This approach allows for flexible, powerful analysis and is foundational in many areas like engineering, physics, and numerical simulations.