A new form of global sensitivity analysis, based on Lie algebraic and group methods appropriate to many problems of chemistry, physics, and engineering, is outlined. An algorithm is provided that enables one to systematically determine, exactly or approximately, operators that convert solutions of ordinary differential equations containing parameters into families of solutions that arise when the parameters in the equation are changed in value. These techniques differ from conventional sensitivity analysis in that the new solutions generated by the present methods are guaranteed to satisfy the transformed differential equation. For example, if one knows a solution valid for some nonzero but restricted range of a parameter in the differential equation, then the operators can be used to obtain solutions valid outside of this range when such exist. If one knows a single solution valid for all values of the parameters, the operators can be used to obtain a many-parameter family of solutions valid for all values of the parameters. The operator determining equations of the present method are shown to reduce to those of conventional sensitivity analysis under appropriate restrictive conditions.
All Science Journal Classification (ASJC) codes
- Physical and Theoretical Chemistry