Howtosignalprocessing
- What is discretization of differential equations?
- What does it mean to discretize an equation?
- How do you discretize Pdes?
- What are the methods of discretization?
What is discretization of differential equations?
A general concept for the discretization of differential equations is the method of weighted residuals which minimizes the weighted residual of a numerical solution. Most popular is Galerkin's method which uses the expansion functions also as weight functions.
What does it mean to discretize an equation?
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.
How do you discretize Pdes?
Discretization: From ODE to PDE
For an ODE for u(x) defined on the interval, x ∈ [a, b], and consider a uniform grid with ∆x = (b−a)/N, discretization of x, u, and the derivative(s) of u leads to N equations for ui, i = 0, 1, 2, ..., N, where ui ≡ u(i∆x) and xi ≡ i∆x.
What are the methods of discretization?
Three discretization methods: the central finite differences, Hermite collocation on finite elements, and the Galerkin finite elements method have been evaluated using a 1D linear differential model.
