The authors consider a two-point boundary value problem of the form \((P\otimes Q)y'+(R\otimes S)y=f(t,y(t))\), \((M\otimes N)y(a)+(U\otimes V)y(b)=a\), where \(P\), \(R\), \(M\), \(U\) are \(m\times n\) matrices, \(Q\), \(S\), \(V\), \(N\) are \(p\times q\), \(y\) is a column matrix of order \(nq\times 1\), \(a\) is \(mp\times 1\), and \(f: [a,b]\times \mathbb{R}^{nq} \to \mathbb{R}^{nq}\) is continuous.
The solution of the Kronecker product nonhomogeneous boundary value problem is first obtained in the form of an integral transform involving a Green matrix. The unique solution of the two-point boundary value problem is constructed by using Banach’s fixed-point theorem. A solution algorithm using the modified Gram-Schmidt process of J. R. Rice [Math. Comput. 20, 325-328 (1966; Zbl 0228.65034)] is presented.