Solving difference equation with its initial conditions

Question

Ben Le 2017-2-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/325773-solving-difference-equation-with-its-initial-conditions

编辑： Ben Le 2017-2-21

采纳的回答： Jan

在 MATLAB Online 中打开

Hi,

Consider a difference equation:

8*y[n] - 6*y[n-1] + 2*y[n-2] = 1

with initial conditions

y[0]= 0 and y[-1]=2

How can I determine its plot y(n) in Matlab? Thank you in advance for your help!

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John D'Errico 2017-2-19

Surely you can use a loop? Why not make an effort? You have the first two values, so a simple loop will suffice.

More importantly, you need to spend some time learning MATLAB. Read the getting started tutorials. It is apparent that you don't know how to even use indexing in MATLAB, nor how to use a for loop.

You will need to recognize that MATLAB does NOT allow zero or negative indices.

Walter Roberson 2017-2-19

I would call this a recurrence equation, not a difference equation.

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Answer 1

Jan 2017-2-21

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https://ww2.mathworks.cn/matlabcentral/answers/325773-solving-difference-equation-with-its-initial-conditions#answer_255734

编辑：Jan 2017-2-21

在 MATLAB Online 中打开

Resort the terms:

8*y[n] - 6*y[n-1] + 2*y[n-2] = 1
y[n] = (1 + 6*y[n-1] - 2*y[n-2]) / 8

or in Matlab:

y(n) = (1 + 6*y(n-1) - 2*y(n-2)) / 8;

Now the indices cannot start at -1, because in Matlab indices are greater than 0. This can be done by a simple translation:

y = zeros(1, 100);  % Pre-allocate
y(1:2) = [2, 0];
for k = 3:100
  y(k) = (1 + 6*y(k-1) - 2*y(k-2)) / 8;
end

Now you get the y[i] by y(i+2).

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Ben Le 2017-2-21

编辑：Ben Le 2017-2-21

Thank you so much, Jan!!!!

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Answer 2

Sindhuja Parimalarangan 2017-2-21

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/325773-solving-difference-equation-with-its-initial-conditions#answer_255713

This link discusses solving recurrence equations using MATLAB. The discrete solution for "y" can be plotted using the stem function.

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