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Basis for Power Series Solutions to Systems of Linear, Constant Coefficient Partial Differential Equations

โœ Scribed by Paul S. Pedersen

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
125 KB
Volume
141
Category
Article
ISSN
0001-8708

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โœฆ Synopsis

Using the theory of generalized functions and the theory of Fourier transforms in several complex variables, previous authors developed a nonconstructive, integral representation for power series solutions to a given system of linear, constant coefficient partial differential equations (PDEs). For a variety of reasons that theory is quite technical. In this paper we describe an algorithm which gives a constructive, countable basis for the set of power series solutions to a given system of linear, constant coefficient PDEs.

๐Ÿ“œ SIMILAR VOLUMES

A Basis for Polynomial Solutions to Syst
A Basis for Polynomial Solutions to Systems of Linear Constant Coefficient PDE's
โœ Paul S. Pedersen ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 261 KB

Let K represent either the real or the complex numbers. Let P k , k=1, 2, ..., r be constant coefficient (with coefficients from K) polynomials in n variables and let r] be the set of all polynomial solutions (of degree M) to this system of partial differential equations. We solve the problem of fi