A very large-scale integration (VLSI) coordinate rotation digital computer (CORDIC) based algorithm and pipelined architecture for solving state-space equations are described. The differential equations can be reduced into a set of linear system equations by an orthogonal polynomial expanded approach. With the advent of VLSI techniques, these linear equations can be implemented in a VLSI chip using a systolic processor array with 0(N2/2) processors. The total computation time is O(4N) time units, which is faster than other conventional methods. From a viewpoint of numerical stability, this algorithm based on circular rotation is superior to the conventional hyperbolic-rotation-based method.