How to set up a system of linear equations with loop and solve it?

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Chong Zhang 2018-5-17

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https://ww2.mathworks.cn/matlabcentral/answers/401304-how-to-set-up-a-system-of-linear-equations-with-loop-and-solve-it

编辑： Torsten 2018-5-18

There is a system of linear equations with 1000 equations and 1000 variables. The 1000 variables are: x(1),x(2),...,x(999),b. The 1000 equations are: 6*x(i)+(1000-i)*(x(i+1)-x(i))-5*x(i+500)=1 (i=0,1,...,499), and x(i)=1+b*(2/3-i*2/3000)^6 (i=500,501,...,999), where x(0)=0.8. How to program this system of linear equations and solve it?

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Chong Zhang 2018-5-18

I revised it. Can you read it now?

Torsten 2018-5-18

编辑：Torsten 2018-5-18

If you understood the solution of the two ODEs that are coupled at x=1/3, you should also come up with a solution of this linear system of equations that is coupled at i=500.

Hint:

The "real" unknown is b which can be determined by making x(500) from the first recursion equal x(500) from the second recursion.

Best wishes

Torsten.

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