Numerical methods are techniques in which mathematical problems are formulated in a way that allows them to be solved using only arithmetic operations such as addition, subtraction, multiplication, and division.
Not every mathematical equation has an analytical (exact) solution. Some equations do not have analytical solutions, and in such cases, numerical methods take on the role of solving them. One example is nonlinear differential equations(Ordinary Differential Equations/ODEs and Partial Differential Equations/PDEs).
Here is an example of a problem that has no exact solution: the Navier-Stokes equations (incompressible flow). \[\frac{\partial u}{\partial t}+(u.\nabla)u=-\nabla p+\nu \nabla^2 u)+f\] \[\nabla . u=0\]
The use of numerical methods to solve the Wave Equation (a Partial Differential Equation of hyperbolic type).
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