In numerical analysis, the local linearization method is a general strategy for designing numerical integrators for differential equations based on a local linearization of the given equation on consecutive time intervals.

What is local linearization of a function?

Summary. Local linearization generalizes the idea of tangent planes to any multivariable function. The idea is to approximate a function near one of its inputs with a simpler function that has the same value at that input, as well as the same partial derivative values.

How do you find the local linearization at a point?

Explanation: The linearization of a differentiable function f at a point x=a is the linear function L(x)=f(a)+f'(a)(x−a) , whose graph is the tangent line to the graph of f at the point (a,f(a)) . When x≈a , we get the approximation f(x)≈L(x) .