Lie-group theory for symbolic integration of first-order differential equations: a modern treatment. [In MACSYMA system]
A review of the present status of the application of Lie-group theory to the solution of first-order ordinary differential equations (ODEs) is given. A code written in the MACSYMA language is presented which finds and solves first-order DOEs invariant under group with infinitesimal generation of the form U = A(x)B(y)delta/sub x/ + C(x)D(y)delta/sub y/. An algorithm is given by which one can begin with an ODE y'= f(x,y) with known solution phi(x,y) = c and obtain a possibly larger class of ODEs with solutions given in closed form. A final algorithm for forming a sequence of solvable differential equations is suggested. The work can be generalized to higher-order differential equations, partial differential equations, and difference equations. 1 table.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6219132
- Report Number(s):
- LA-UR-79-251; CONF-790629-2
- Resource Relation:
- Conference: 2. MACSYMA users conference, Washington, DC, USA, 20 Jun 1979
- Country of Publication:
- United States
- Language:
- English
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