The Green’s function method of sensitivity analysis in chemical kinetics

Abstract

A new approach to the sensitivity analysis of large computational models is presented. The basis for the method is the well-known Green’s function technique. By working with the same differential equations as the conventional direct method, this new approach reduces the number of differential equations to be solved and replaces them by a set of integrals. Altogether, there is only one set of differential equations in the Green’s function method, regardless of the number of system parameters m. Sensitivity coefficients of all orders are expressed in integral form and evaluated in a recursive manner. Since evaluating well-behaved integrals is usually much easier than solving stiff differential equations, substantial savings can be achieved by the method when the number of system parameters is large. It is estimated that if only linear sensitivity coefficients are desired, then the Green’s function method could be advantageous for the case m≳n, where n is the number of dependent variables. However, if both linear and higher order sensitivity coefficients are to be computed, the method could be competitive with other approaches even when m<n. A numerical calculation on a simple linear system is presented to provide a brief illustration of the method.