Unrestricted Harmonic Balance A General Method to Evaluate Periodic Structures in T ime and/or Space of Arbitrary Stability for Non-linear Chemical Reaction and Reaction-Diffusion Systems IV. Extension to Transcendental Functions

The method of Unrestricted Harmonic Balance (UHB) as exposed and applied to purely t imedependent systems, stiff systems, and chemical waves in the preceding 3 papers is extended to the case of transcendental functions. So, e.g., exponential functions even in mass action kinetics systems occur, if a wider range of temperature is considered as is the case in continuous stirred tank reactors (CSTR). Here the reaction heat is removed by heat exchangers, but since the volume is in most cases considerable, the system cannot be kept strictly isothermal and instabilities are known to arise. Here the oscillatory case is treated with the method of UHB.