Numerical Integration of Systems of Stiff Nonlinear Differential Equations

In connection with the design of transistor circuits, for example, it is often necessary to obtain a numerical solution of a system of nonlinear differential equations x -f- f(x, t) = 0, t* 0, [x(0) = x0] (1) in which x and f(x, ·) are N-vector-valued functions of t. The simplest numerical-integration formula which can be in principle used for this purpose is Euler's formula: yn+1 = Vn + hy'n , y'n = -f(yn , nh) for n ^ 0 n ^ 0; (2)