R69-21 Hybrid Assumed Mode Solution of Non-Linear Partial Differential Equations

Readers of this paper are likely to come away with too narrow a view of the little-known and little-appreciated art of assumed mode methods for solving distributed parameter system problems. The fact that only three references to these methods are cited is evidence of the wide scattering of the many papers which have appeared concerning these methods. The papers cited at the end of this review have been carefully selected to enable the reader to enter the most recent literature on a broader front. There the reader will find many more assumed mode methods than just the Galerkin method (which is the only one mentioned by Newman and Strauss). The reader will also find, contrary to an assertion by the authors, that assumed mode methods do not offer equal accuracy with fewer equations, as compared with nodal methods [1], although this possibility exists when a problem involves only a restricted class of system behaviors [2]. The literature also contains examples of nonlinear problems which have been solved on analog computers by assumed mode methods, e.g., [2], which the authors apparently had not encountered.