In MATLAB, usually we use function bvp4c() to solve boundary value problem (BVP) of ODE. However, we also can use function ode45() to solve BVP of ODE too. However, ode45() needs all initial values at one point. Therefore we have to construct an auxiliary function, whose input argument is the missing initial value and the return output is the given boundary value, Then we can call function fsolve() to get the missing initial value. This method is particularly efficient it the ODE has one or more parameters. Also this method is essentilal for GNU Octave, because whose function bvp4c() is not programmed for parameter ODE yet.

How Use ODE45 to solve Boundary Value ODE.pdf

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