Partial Differential Equation

The wave equation is a second-order linear partial differential equation that describes mechanical waves (e.g., water waves, sound waves, and seismic waves) and light waves as they arise in classical physics. Acoustics, electromagnetics, and fluid dynamics are examples of domains that can occur.

Solving PDEs is generally based on finding a transformation of a variable to transform the equation into something soluble or on finding an integral form of the solution. 

a ∂u ∂x + b ∂u ∂y = c. dy dx = b a , and ξ(x, y) independent (usually ξ = x) to alter the PDE into an ODE.

The 2nd derivative of the dependent variable is expressed as a function of the variable, and its 1st derivative is a second-order differential equation.

In general, partial differential equations are much tougher to solve than ordinary differential equations.

Pp + Qq = R, where P, Q, and R are functions of x, y, and z, is a Quasi-linear partial differential equation of order one. The Lagrange equation is a type of partial differential equation like this. A Lagrange equation is something like xyp + yzq = zx.

Finite difference and finite volume methods are used to discretize partial differential equations in CFD. The flow variables are obtained by solving these discretized equations simultaneously. You can always learn more with https://www.mygreatlearning.com

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