Numerical Methods for Weather Forecasting Using Mathematical Models
Abstract
Weather forecasting plays an important role in modern society because accurate predictionshelp governments and industries prepare for natural events and environmental changes. The behaviour of the atmosphere is governed by complex physical laws that are represented by mathematical equations. These equations are nonlinear and cannot usually be solvedanalytically. Numerical methods provide computational techniques to approximate solutions of these equations using digital computers. This paper presents an overview of the mathematical models and numerical algorithms used in modern weather forecasting systems.The Navier– Stokes equation, continuity equation, and heat diffusion equation are discussed as fundamental models of atmospheric motion. Numerical methods such as finite difference, Runge–Kutta integration, interpolation,
and iterative solvers are described in detail. Simulation graphs and computational diagrams illustrate how numerical algorithms predicttemperature, pressure, and wind patterns. The study demonstrates the importance ofmathematical modelling and computational science in numerical Weather prediction.
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