Solving Third Order Differential Equations with Maximal Symmetry Group |
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Authors: | Fritz Schwarz |
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Affiliation: | GMD, Institute SCAI Schlo? Birlinghoven 53754 Sankt Augustin Germany e-mail: fritz.schwarz@gmd.de, DE
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Abstract: | The largest group of Lie symmetries that a third-order ordinary differential equation (ode) may allow has seven parameters. Equations sharing this property belong to a single equivalence class with a canonical representative v ′′′(u)=0. Due to this simple canonical form, any equation belonging to this equivalence class may be identified in terms of certain constraints for its coefficients. Furthermore a set of equations for the transformation functions to canonical form may be set up for which large classes of solutions may be determined algorithmically. Based on these steps a solution algorithm is described for any equation with this symmetry type which resembles a similar scheme for second order equations with projective symmetry group. Received March 9, 2000; revised June 8, 2000 |
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Keywords: | AMS Subject Classifications: 34A05 34A25 34B30 68Q40. |
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