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How to Solve an ODE Problem when one of parameters is dependent to derivative? 
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#1
Apr212, 01:23 AM

P: 4

Hello Guys!
I have an ODE problem that I'm solving it by MATLAB ODE solvers! in fact I have a system of nonlinear differential equations in one of these equations I have a parameter that it's value is dependent to derivative! the general form of equation is like this (big letter parameters are known!): dy/dt = A + B + f(C,D,dy/dt) how can I solve this problem by ode45 or other MATLAB ODE solvers? 


#2
Apr312, 05:17 PM

HW Helper
P: 1,583

Is the function f known?



#3
Apr312, 10:14 PM

P: 4

but it's not reversible 


#4
Apr412, 02:42 AM

P: 759

How to Solve an ODE Problem when one of parameters is dependent to derivative?
Let X= dy/dt . X is solution of the equation X = A + B + f(C, D, X) wich is not an ODE. It doesn't matter if the function is not revertsible. We don't need to know the analytical expression of the solution(s) X. We know that dy/dt = constant (or = several different constants if there are several solutions). Each one can be numerically computed, not using an ODE solver, but using an usual numerical equation solver. The solution(s) is (are) : y(t) = X*t +c c is a constant to be determined by the boundary condition. 


#5
Apr412, 02:55 AM

P: 4

A and B and C and D are NOT constant parameters! I did't write them because they were not necessary! in fact You don't need to know what's the equation exactly to answer my question! My question is simple: MATLAB ODE solvers solve equations in form of dy/dt=f(t,y) but I want to solve an equation in form of dy/dt=f(t,y,dy/dt) ... How I can do that by MATLAB? 


#6
Apr412, 03:29 AM

P: 759

May be, you could use an algorithm of this kind: Start with given initial values y and t. Recursive process : Compute A(y,t), B(y,t), C(y,t) and D(y,t) Solve X=A+B+f(C,D,X) with a numerical equation solver, introduced as subprogram. With the computed value X=dy/dt the incrementation of y is done, as well as the incrementation of t. Then continue the recursive process. 


#7
Apr412, 03:31 AM

P: 4




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