Solving complex-valued differential systems

摘要

Linear two-point boundary-value problems defined in complex space arise frequently in physical studies. We examine initial-value procedures based on superposition principles applied to the associated real system of equations. We show how to take advantage of the fact that the underlying problem is complex, thereby cutting the usual number of necessary integrations of the homogeneous system by one-half. We also discuss several aspects of incorporating these ideas into a computer code utilizing an orthonormalization procedure.