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Computer Science - Theoretical Computer Science | Loewy Decomposition of Linear Differential Equations

Loewy Decomposition of Linear Differential Equations

Schwarz, Fritz

2012, XVI, 232 p.

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  • Most advanced and most complete text on closed form solutions of linear partial differential equations 
  • Provides more than 50 worked out examples and exercises including solutions 
  • The results described in the book may be applied for determining Lie symmetries of nonlinear differential equations
The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

Content Level » Research

Keywords » Computer Algebra Software - Differential Algebra - Partial Differential Equations

Related subjects » Computational Intelligence and Complexity - Dynamical Systems & Differential Equations - Theoretical Computer Science

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