## Algorithms for the solution of systems of coupled second order ordinary differential equations |

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6-graph accuracy applied approximately asymptotic atomic units ATOMNP auxiliary functions boundary conditions channels Chapter characteristic polynomial coefficients computer storage Computing-times convergence corrector cross section defined denotes derivatives DeVogelaere direct integration double precision error propogation f Xn+ F(Xn form Yn+1 graph H2 f Hence Henrici 54 higher order Hybrid methods inner region instability integrating algorithm integrating method interpolating interpolation formula interval interval arithmetic iq(i iterative linearly independent linearly independent solutions matrix modulus multi-step methods notation NTOT NTOT+NA Numerov algorithm Numerov method Nystrom one-step methods order differential equation order Runga-Kutta method Order Systems ordinary differential equations origin parameters particular predictor-corrector reduced replacement resonance resultant round-off error S-matrix Scraton second order equations step step-size storage requirements system of coupled system of equations Table Taylor series solution term Theorem truncation error vector Vogelaere method wave function zero