Computational physics

Computational physics uses numerical algorithms and computer simulations to study physical systems when analytic solutions or direct experiments are impractical.

Numerical analysis: The study of algorithms for approximating mathematical problems and controlling their errors. Its error analysis and stability tools determine whether a physical simulation is trustworthy.
Partial differential equation: An equation involving an unknown function and its derivatives with respect to multiple variables. Many physical laws are expressed as partial differential equations before discretization.
Computational fluid dynamics: The numerical study of fluid flow using discretized equations of motion. It predicts flows around aircraft, through engines, and across environmental systems.
Analytical solution: An exact or symbolic solution expressed through mathematical reasoning rather than numerical approximation. It can provide exact insight where a simulation supplies only approximate values.
Finite difference method: A numerical method that approximates derivatives using values at discrete points. It turns differential equations in many physical models into solvable algebraic updates.
Ordinary differential equation: An equation relating a function of one variable to its derivatives. Time evolution of particles and other dynamical systems often reduces to these equations.
Climate model: A mathematical representation of Earth's climate system used to simulate its behavior and changes. Numerical simulations combine atmosphere, ocean, land, and ice processes to project climate.
Experimental physics: The branch of physics that investigates nature through observation and controlled experiments. Experiments measure physical systems directly, while simulations calculate consequences of models.
Finite element method: A numerical method that approximates solutions to differential equations by dividing a domain into smaller elements. It handles complex geometries and boundary conditions in structural and continuum simulations.
Boundary condition: A constraint specifying a solution's behavior at the boundary of a domain. Simulations need boundary conditions to define how modeled regions interact with their surroundings.

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