Recognising and Solving Special Function ODEs
نویسنده
چکیده
Code to recognise and hence solve the second-order linear ODEs that define the special functions of mathematical physics is being developed for the Reduce ODE solver. It allows an arbitrary, possibly symbolic, affine transformation of the independent variable. At first sight, the problem appears to be one of pattern matching or table look-up, but simple special-purpose code written for each class of ODEs turns out to be more appropriate than use of a general pattern matcher. The technique used is successive analysis of the coefficient functions after dividing through by the coefficient function of the leading derivative. This canonicalizes the ODE and allows the ODE class and the transformation to be determined together.
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