Algorithmic Lie Theory for Solving Ordinary Differential Equations

ISBN: 9781584888895 出版年：2007 页码：446 Schwarz, Fritz CRC Press

INTRODUCTION LINEAR DIFFERENTIAL EQUATIONS Linear Ordinary Differential Equations Janet's Algorithm Properties of Janet Bases Solving Partial Differential Equations LIE TRANSFORMATION GROUPS Lie Groups and Transformation Groups Algebraic Properties of Vector Fields Group Actions in the Plane Classification of Lie Algebras and Lie Groups Lie Systems EQUIVALENCE AND INVARIANTS OF DIFFERENTIAL EQUATIONS Linear Equations Nonlinear First-Order Equations Nonlinear Equations of Second and Higher Order SYMMETRIES OF DIFFERENTIAL EQUATIONS Transformation of Differential Equations Symmetries of First-Order Equations Symmetries of Second-Order Equations Symmetries of Nonlinear Third-Order Equations Symmetries of Linearizable Equations TRANSFORMATION TO CANONICAL FORM First-Order Equations Second-Order Equations Nonlinear Third-Order Equations Linearizable Third-Order Equations SOLUTION ALGORITHMS First-Order Equations Second-Order Equations Nonlinear Equations of Third Order Linearizable Third-Order Equations CONCLUDING REMARKS APPENDIX A: Solutions to Selected Problems APPENDIX B: Collection of Useful Formulas APPENDIX C: Algebra of Monomials APPENDIX D: Loewy Decompositions of Kamke's Collection APPENDIX E: Symmetries of Kamke's Collection APPENDIX F: ALLTYPES Userinterface REFERENCES INDEX