Concept explainers
Show that Euler’s method applied to the differential equation
yields Eq. (1) in the absence of random disturbances, that is, when
To prove: The Euler’s method applied to the differential equation
Explanation of Solution
Given information:
The differential equation
Formula used:
Euler’s method: Suppose the solution of the initial value problem
So, the approximation for
Proof:
Let the differential equation is
By using Euler’s method,
Here
The solution of the differential equation
A discrete model for change in the price of a stock over a time interval
If the value of the random disturbance is absent in the discrete model that is the value of
Thus the discrete model becomes,
Therefore, the differential equation
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Differential Equations: An Introduction to Modern Methods and Applications
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