Euler's Method Calculator With Steps

What is Euler's Method?

The Euler's method is a start-order numerical process for solving ordinary differential equations (ODE) with a given initial value.

The General Initial Value Trouble

Methodology

Euler'south method uses the simple formula,

to construct the tangent at the point x and obtain the value of y(x+h), whose slope is,

In Euler's method, yous can gauge the curve of the solution by the tangent in each interval (that is, by a sequence of brusk line segments), at steps of h.

In general, if you use small-scale footstep size, the accurateness of approximation increases.

General Formula

Functional value at any point `b`, given by `y(b)`

where,

n = number of steps
h = interval width (size of each step)

Pseudocode

Example

Detect y(1), given

Solving analytically, the solution is y = e^x and y(1)= two.71828. (Note: This analytic solution is just for comparing the accurateness.)

Using Euler's method, because h = 0.2, 0.1, 0.01, you tin can encounter the results in the diagram below.

When h = 0.2, y(1) = 2.48832 (error = 8.46 %)

When h = 0.1, y(1) = 2.59374 (error = 4.58 %)

When h = 0.01, y(1) = 2.70481 (fault = 0.fifty %)

You can notice, how accuracy improves when steps are small.

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