Subject: solve system of nonlinear differential equations
From: Ether Jones
Date: Mon, 10 Dec 2012 07:38:55 -0800 (PST)
Sorry, I should have been clearer.? The functions f1() and f2() are non-linear.? How does the experienced Maxima user go about setting up the *numerical* solution?? I want to graph the solution from t=0 to t=T, where T is some constant number I select.?
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From: Jaime Villate <villate at fe.up.pt>
To: Ether Jones <maxima at etherjones.us>
Cc: maxima <maxima at math.utexas.edu>
Sent: Monday, December 10, 2012 4:38 AM
Subject: Re: [Maxima] solve system of nonlinear differential equations
On 12/10/2012 05:33 AM, Ether Jones wrote:
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>diff(x,t,2) = f1(diff(x,t),diff(y,t));
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>diff(y,t,2) = f2(diff(x,t),diff(y,t));
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>initial conditions at t=0:
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>x:Xo;? y:Yo;? diff(x,t):Vxo;? diff(y,t): Vyo;
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>Please, What is the most expedient method for solving the above system of differential equations using Maxima?
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It depends on the particular functions f1 and f2 that you are interested in. I think there is no general method. If f1 and f2 are linear, you might look for an analytic solution, while for other functions you can only find an approximate numerical solution.
Regards,
Jaime