Schwarz, Fritz.
Loewy Decomposition of Linear Differential Equations [electronic resource] / by Fritz Schwarz. - XV, 230 p. 1 illus. online resource. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 0943-853X . - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
Loewy's results for ordinary differential equations -- Rings of partial differential operators -- Equations with finite-dimensional solution space -- Decomposition of second-order operators -- Solving second-order equations -- Decomposition of third-order operators -- Solving third-order equations -- Summary and conclusions -- Solutions to the exercises -- Solving Riccati equations -- The method of Laplace -- Equations with Lie symmetries.
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.
9783709112861
10.1007/978-3-7091-1286-1 doi
Computer science.
Algebra--Data processing.
Differential equations, partial.
Engineering mathematics.
Computer Science.
Symbolic and Algebraic Manipulation.
Partial Differential Equations.
Appl.Mathematics/Computational Methods of Engineering.
QA76.9.M35
005.131
Loewy Decomposition of Linear Differential Equations [electronic resource] / by Fritz Schwarz. - XV, 230 p. 1 illus. online resource. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 0943-853X . - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
Loewy's results for ordinary differential equations -- Rings of partial differential operators -- Equations with finite-dimensional solution space -- Decomposition of second-order operators -- Solving second-order equations -- Decomposition of third-order operators -- Solving third-order equations -- Summary and conclusions -- Solutions to the exercises -- Solving Riccati equations -- The method of Laplace -- Equations with Lie symmetries.
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.
9783709112861
10.1007/978-3-7091-1286-1 doi
Computer science.
Algebra--Data processing.
Differential equations, partial.
Engineering mathematics.
Computer Science.
Symbolic and Algebraic Manipulation.
Partial Differential Equations.
Appl.Mathematics/Computational Methods of Engineering.
QA76.9.M35
005.131