Time complexity notation for when you don't know the complexity of something

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I am working with a piece of software that creates a system of differential equations in Matlab, that it then runs through the $textrmode15s$ differential equation solver. I know that the system that is generated generates at $mathcalO(mn)$ for a system that is given by two variables $m,n$.



However I have no idea what the time complexity of $textrmode15s$ is (although if anyone knew that that'd be very helpful), so I wanted to know if there was a way to write that the time complexity is based on the size of my system run through $textrmode15s$.



For example, imagine that for a system of size $k$, $textrmode15s$ ran with complexity $mathcalO(g(k))$, can I then say that my system runs with complexity $mathcalO(g(mn))$?




notation computational-complexity programming




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    I am working with a piece of software that creates a system of differential equations in Matlab, that it then runs through the $textrmode15s$ differential equation solver. I know that the system that is generated generates at $mathcalO(mn)$ for a system that is given by two variables $m,n$.



    However I have no idea what the time complexity of $textrmode15s$ is (although if anyone knew that that'd be very helpful), so I wanted to know if there was a way to write that the time complexity is based on the size of my system run through $textrmode15s$.



    For example, imagine that for a system of size $k$, $textrmode15s$ ran with complexity $mathcalO(g(k))$, can I then say that my system runs with complexity $mathcalO(g(mn))$?




    notation computational-complexity programming




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      I am working with a piece of software that creates a system of differential equations in Matlab, that it then runs through the $textrmode15s$ differential equation solver. I know that the system that is generated generates at $mathcalO(mn)$ for a system that is given by two variables $m,n$.



      However I have no idea what the time complexity of $textrmode15s$ is (although if anyone knew that that'd be very helpful), so I wanted to know if there was a way to write that the time complexity is based on the size of my system run through $textrmode15s$.



      For example, imagine that for a system of size $k$, $textrmode15s$ ran with complexity $mathcalO(g(k))$, can I then say that my system runs with complexity $mathcalO(g(mn))$?




      notation computational-complexity programming




      share|cite|improve this question











      I am working with a piece of software that creates a system of differential equations in Matlab, that it then runs through the $textrmode15s$ differential equation solver. I know that the system that is generated generates at $mathcalO(mn)$ for a system that is given by two variables $m,n$.



      However I have no idea what the time complexity of $textrmode15s$ is (although if anyone knew that that'd be very helpful), so I wanted to know if there was a way to write that the time complexity is based on the size of my system run through $textrmode15s$.



      For example, imagine that for a system of size $k$, $textrmode15s$ ran with complexity $mathcalO(g(k))$, can I then say that my system runs with complexity $mathcalO(g(mn))$?





      notation computational-complexity programming





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      share|cite|improve this question




      share|cite|improve this question









      asked Aug 1 at 16:19









      wjmccann

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