Dirac’s formalism combined with complex Fourier operational matrices to solve initial and boundary value problems.

Highlights: [•] Methods based on series approximations are useful for differential equations. [•] Projections in a Hilbert space basis, combined with optimization algorithms, provide precise solutions. [•] Dirac’s formalism allows extensions for complex functions. [•] Fourier decomposition provides a simple and precise algorithm to solve differential equations. [•] Precision is considerably improved by using this kind of method. [ABSTRACT FROM AUTHOR]