Solving a differential Equation in matrix form

Mohi

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Oct 5, 2016
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Hello,

I am working on a math equation which involves a differential which is combined in matrix form. It would be helpful if someone can help me in solving this equation.

The variables of this equation are Ra1(n|t) and Ra2(n|t) are probabilities of scoring n goals in time t.
a10, a12,a21,a23 are transition probabilities.

I have attached the image of the equation for better view as typing it might make it ambiguous.

attachment.php
 

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Solving the differential equation in matrix form

I am trying to solve a differential equation which is in matrix form

d/dt(Ra1(n|t) = (-a10-a12 a12 ) * ( Ra1(n|t) ) + (0 a10 ) * ( Ra1(n-1|t) )
Ra2(n|t) ) a21+a23 -a21-a23 Ra2(n|t) 0 0 Ra2(n-1|t)


Ra1 and Ra2 are probabilities of n goals in remaining time t. a12 = 0.073, a12=3.3 ,a21 = 3.0, a23 =0.041.

This equation gives probability distribution over time t. While I have the values of a12, a21,a23 and so on I am not sure how to handle the Ra1 and Ra2 values.

I am attaching a picture of the equation.

it would be great if someone can give me some idea, as to how to get through the Ra1 and Ra2.

Thanks.
attachment.php
 

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  • Screen Shot 2016-10-05 at 10.34.37 AM.jpg
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