A new closed-form expression for the solution of ODEs in a ring of distributions and its connection with the matrix algebra

A new Legendre polynomial-based approach for non-autonomous linear ODEs

“…Section 2.1 discusses the expansion of functions and distributions in the basis of orthonormal Legendre polynomials and defines the coefficient matrix. In Section 2.2, the connection between the -product and the matrix algebra is used to reformulate the problem in (1.1) as an infinite matrix problem; see also [31].…”