Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization

Abstract

We discuss algorithmic matters of a computer code for solving linear two-point boundary-value problems. The method of solution uses superposition coupled with an orthonormalization procedure and a variable-step Runge–Kutta–Fehlberg integration scheme. Each time the linearly independent solutions start to lose their numerical independence, the vectors are reorthonormalized before integration proceeds. The underlying principle of the algorithm is then to piece together the intermediate (orthogonalized) solutions, defined on the various subintervals, to obtain the desired solution.