Rapid Solution of Stiff Differential Equations and Accurate Numerical Laplace Inversion of Steep and Oscillatory Functions using I MN Approximants

I MN approximants are a fast and convenient method of solving initial value problems in linear stiff differential algebraic equations as well as obtaining the numerical inversion of Laplace transforms In the past it was impossible to use them to obtain sufficiently accurate inversions of certain steep and highly oscillatory responses as useable values of N had to be relatively small not only to ensure reliable evaluation of I MN constants but also in order to avoid undue rounding errors in the computed results However, the development of computer algebra systems such as Mathematica which permit infinite precision computation has provided greater latitude for the application of the method This work is an exposition of the potency of I MN approximants in accurately and cheaply inverting functions in the Laplace domain whose time functions are steep, oscillatory or stiff Previous applications of the method to some examples in the literature led to wrong conclusions as the capabilities of the method were not fully explored We show how to obtain very accurate results in these circumstances using both the global and step‐by‐step methods The results of using I MN step‐by‐step technique to rapidly solve stiff differential equations of a large staged process are also presented As Matlab gives inaccurate results, Mathematica has been used to compute both the transfer function and the analytical expression for the time response of the plant Extended values ofM and N as well as the ranges of the corresponding I MN constants are tabulated for I MN approximants of full grade.