An efficient algorithm reduces computing time in solving a system of stiff ordinary differential equations

The problem of stiff differential equations arises in many computer-aided design techniques, particularly in the transient analysis of network simulation. Special multistep methods are used to solve the first-order stiff nonlinear differential equations. Instability and a large number of steps are encountered during simulation. Different techniques such as step and order selection schemes, procedures for changing step and order, may reduce the number of steps while preserving stability. An improved algorithm is presented using BDF formulas given by Brayton et at. and leads to reducing computer time by controlling the number of integration steps, but also the number of Newton iterations, the number of Jacobian matrix evaluations and other parameters, without producing additional errors or instability phenomena. Experimental results are shown.