Start with an initial point (x0, y0) on the solution curve.The basic procedure for Euler's method is as follows: The tangent line is determined by the slope of the solution curve at that point, which is given by the derivative of the solution function. The method starts with an initial point on the solution curve, and then generates a sequence of points by moving along the tangent line at each point. It is a simple and easy-to-implement method that is widely used in physics, engineering, and other fields.Įuler's method is based on the idea of approximating the solution curve of a differential equation by a sequence of straight lines. □ Shorthand Summary of the MethodĮuler's method is a first-order numerical procedure for approximating a solution to a differential equation. This means that x = 7 corresponds to y = 249, which is our approximate solution. As an exercise, find an approximate value for y(9). Note that as the step size approaches zero, the approximation becomes more and more exact.
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