[tex]{\frac {{\it du}}{{\it dx}}}=998\,u+1998\,v [/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]{\frac {{\it dv}}{{\it dx}}}=-999\,u-1999\,v [/tex]

[tex]u \left( 0 \right) =1 [/tex]

[tex]v \left( 0 \right) =0 [/tex]

0<x<10

Second Order Backward Difference formula

[tex]{\frac {f_{{k-2}}-4\,f_{{k-1}}+3f_{{k}}}{h}}[/tex]

I'm trying solve this numerically in matlab, but can't seem to figure out what to do with the k-2 indice in the 2nd order backward difference equation, because it is outside the boundary. I was thinking of using a ficticious or ghost point, but I thought that only applies if a neuman boundary condition is given. The way i think of it, I have 4 unknowns and only 2 equations.

EDIT: ok after thinking about it. I think I have to use another numerical method to start the process, like RK4.

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# System of ODE Boundary Value Problem with 2nd Order Backward Difference

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