Power series solutions for non-linear PDE's

ABSTRACT

This paper describes an algorithmic method iterative method for searching power series solutions of a partial differential equation. Power series expansions considered have support in some convex cone of R^N. We do this by introducing a N-variables analog of the Newton polygon construction, used in the case of ordinary differential equations.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

General Terms:
Algorithms

Keywords:
Newton polyhedron, PDE's, fractional power series solutions