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Numerically Solving ODE with Lagrange Multipliers
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Mar1-10, 10:07 AM
I'm trying to implement some equations from a paper. It comes down to a system of 2 coupled ODEs. In one of the ODEs, there are 3 Lagrange multipliers. The paper says that the three multipliers can be determined by three integral constraints (integrals of some functions of the solutions of the ODEs are equal to some value). I don't get how this can be numerically solved with any degree of efficiency. It appears to solve the ODEs you need to know the value of the Lagrange Multipliers, but to evaluate the Lagrange multipliers you need to know the solution of the ODE. My supervisor isn't too forthcoming with help - it seems he's very busy. The only way I can think of this solving this is to a try thousands of random multipliers and retain the multipliers which return the smallest error against the three defined constraints. Is there some common magical numerical technique for solving equations of this type? I presume there is as the paper from which I got the equations describes this part in little detail.
I can provide the functions and integrals in question, if necessary. I apologise if any parts were unclear. As you probably know, it's sometimes hard to describe maths with words.
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