Finding hyperexponential solutions of linear ODEs by numerical evaluation

ABSTRACT

We present a new algorithm for computing hyperexponential solutions of linear ordinary differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic functions and evaluating them numerically at some common ordinary point. The numerical data is used to determine a small number of combinations of the formal series that may give rise to hyperexponential solutions.

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Index Terms

• Computing methodologies

  • Symbolic and algebraic manipulation

    • Symbolic and algebraic algorithms