Calculating an integral of two numerical solutions of an ode -


i calculate integral, determined 2 functions: i(t) = ∫0t i( f(t), g(t)) dt f , g solves ordinary differential equations , i known.

the obvious approach derive differential equation i , solve alongside f , g (which can done, numerically expensive in case). in case, however, f solves equation initial condition f(0) , g , equation final condition g(t).

my best guess @ moment solve f , g on grid using standard ode solver , use standard method numerical integration equally spaced t-coordinates or kind of quadrature rule (basically described numerical recipes).

does have better solution? is, method takes specific type of ode solver , accuracy account.

many advanced ode solvers come feature called "dense output". ode solver gives not values of f , g on grid (as specified beforehand), allows use result find values @ time. combining adaptive quadrature rule should give answer whatever precision need.


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