# Integrate nonlinear system of equations using explicit method

I have a system of equations with 3 variables (P,V, and T). The system has one degree of freedom so if I specify P I can solve for V and T. I need to find V and T over a wide range of P. Right now, I just solve for V and T and each P value. However, I would like to use some of MATLAB's ODE methods. Is this possible even though I can not write analytical derivatives for V and T?

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 Wait, wait, you have coupled nonlinear differential equations? Why not post the actual system of DEs? – J. M. May 6 '11 at 3:33 No, I don't have the differentials - only the equations for the actual values. It takes a while to solve them however, I was wondering if there was a way to use the solutions for the equations at a starting point and then integrate instead of just solving at each value of P – Brian May 6 '11 at 3:58 Hi, Brian, if you only have data points, I suggest you try curve fitting toolbox rather than use matlab built-in ode45, could you elaborate your problem a little bit more please? – Shuhao Cao May 6 '11 at 4:01 Alright... so P is the independent variable and V and T are the dependent variables? Do you have expressions for $\frac{\mathrm dV}{\mathrm dP}$ and $\frac{\mathrm dT}{\mathrm dP}$, if you are intending to set up an ODE system? – J. M. May 6 '11 at 4:01 I have two equations 0=f1(P,V,T) and 0=f2(P,V,T) It takes quite a while to solve the system for a given P. I was wondering if there was a way to solve at an initial point and then integrate without solving the system – Brian May 6 '11 at 7:37