Solution to boundary value problems using the method of maximum entropy

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Abstract
The method of maximum entropy is used to solve a class of linear boundary value problems. The method is based on using various moments of the differential equation as constraints when maximizing the entropy. Various examples are presented and compared to exact solutions for varying numbers of moments. It is found that the maximum entropy approximation is, in many cases, better than a Fourier series solution for a given number of expansion terms and moments. The method is very general and will find applications in many areas of physics. A comparison of the amount of work necessary for the maximum entropy solution versus finite difference techniques is presented and it is found that the maximum entropy technique shows promise as an alternative solution technique.

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