Question

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.

The method of approximation known as Euler’s method, including the iterative formula that describes a new coordinate point $(x_{k+1},y_{k+1})$in terms of the previous point $(x_k,y_k)$.

Short answer

Euler's method is a first-order numerical procedure for solving ordinary differential equations.

Step-by-step solution

Step 1. Given Information.

We have to define the approximation known as Euler's method.

Step 2. Euler's method.

Euler's method is a first-order numerical procedure for solving ordinary differential equations with a given initial value.

The formula used is,

$y(x+h)=y\left(x\right)+hf(x,y)$.