To solve two 2nd order coupled differential equation using ODE45?

I have the the following 2nd order differential equation that is needed to be solved.

..............(1)

....................(2)

The initial state are [3 9] for and respectively.

The time interval is [0: 0.05: 1] i.e 21 time steps.

The and are functions of time available for initial 20 time steps (can take as ones for working example).

I don't have any prior experince with ODE45 . Any guidance to solve this problem will be appreciated.

Answer 1

[Alan Stevens]

Replace each 2nd order ODE by two 1st order ODEs. e.g. set V1 = X1', V2 = X2', then V1' = (50*sin(f(t) - V1)*V2')/sin(f(t)), V2' = g(t) - etc.

You will also need initial conditions for V1 (X1') and V2 (X2') as well as for X1 and X2.

help ODE45 % for further details.

[Star Strider]

@Rohit Singh — If you have the Symbolic Math Toolbox, use odeToVectorField and matlabFunction to do the ‘heavy lifting’ to create the function necessary to use the numeric differential equation solvers. They make it easier, and eliminate the possibility of algebra errors.

There are myriad examples in MATLAB Asnwers.

.

[Rohit Singh]

Thank you @Star Strider for the guidance.