APL And The Numerical Solution Of High-Order Linear Differential Equations

An Nth‐order linear ordinary differential equation is rewritten as a first‐order equation in an N×N matrix. Taking advantage of the matrix manipulation strength of the APL language this equation is then solved directly, yielding a great simplification over the standard procedure of solving N coupled first‐order scalar equations. This eases programming and results in a more intuitive algorithm. Example applications of a program using the technique are given from quantum mechanics and control theory