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例子Questions
例子Question #1 :Euler's Method
Suppose we have the following differential equation with the initial condition:
Use Euler's method to approximate, using a step size of.
We start at x = 0 and move to x=2, with a step size of 1. Essentially, we approximate the next step by using the formula:
.
So applying Euler's method, we evaluate using derivative:
And two step sizes, at x = 1 and x = 2.
And thus the evaluation of p at x = 2, using Euler's method, gives us p(2) = 2.
例子Question #11 :Applications Of Derivatives
Approximateby using Euler's method on the differential equation
with initial condition(which has the solution) and time step.
Using Euler's method with意味着我们使用两个迭代得到约imation. The general iterative formula is
where eachis
is an approximation of, and, for this differential equation. So we have
So our approximation ofis
例子Question #3 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
Note: Solving this differential equation analytically gives a different answer,. Future problems will explain this discrepancy.
例子Question #4 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
Note: Solving this differential equation analytically gives a different answer,. As the step size gets larger, Euler's method gives a more accurate answer.
例子Question #5 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
例子Question #6 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
Note: Due to the simplicity of the differential equation, Euler's method finds the exact solution, even with a large step size, Using a smaller step size is unnecessary and more time consuming.
例子Question #7 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
例子Question #8 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
例子Question #9 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
例子Question #10 :Euler's Method
Use Euler's method to find the solution to the differential equationatwith the initial conditionand step size.
Euler's method uses iterative equations to find a numerical solution to a differential equation. The following equations
are solved starting at the initial condition and ending at the desired value.is the solution to the differential equation.
In this problem,
Starting at the initial point
We continue using Euler's method until. The results of Euler's method are in the table below.
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