The computer generated symbolic solution of a system of linear first order differential equations (Q911712)

The authors investigate the matrix differential equation \(dx/dt =Ax\) for an arbitrary \(n\times n\) matrix A and arbitrary initial conditions on x. A computer generated symbolic polynomial solution is obtained using the PL/I-FORMAC interpreter. The generated solution is a polynomial whose degree k is larger than the order of A. The Leverrier method is then used to generate the characteristic polynomial of A and the Cayley-Hamilton theorem is used to reduce powers of A in the solution. The method was tested on randomly generated A for various values of n and k. Numerical results are reported.