## Self-starting multistep methods for the numerical integration of ordinary differential equations |

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algorithms for starting Ames Research Center ap,k automatic computers backward difference equations backward ordinate equations backward starter discussed backward sums Bashforth basic backward difference basic difference equations bootstrap starter coefficients corrector is yn+i corrector ref Cowell corrector derived differences at f0 differences of f0 equa equations 15 equations 23 EQUATIONS By William equations l6 formally as infinite FORTRAN Forward Integration Problem forward integration procedures forward ordinates forward starter FORWARD STARTING ALGORITHMS Henrici ref infinite series initial values integration of systems iterated starter k=o q Moffett Field Multiple corrector nested DO LOOP Newton's interpolating polynomial normal form notation numerical integration obtained ORDINARY DIFFERENTIAL EQUATIONS predictor ref PREDICTOR-CORRECTOR ALGORITHMS programming language q backward recurrence relation right members rithms round-off error second sums SELF-STARTING MULTISTEP METHODS self-starting procedures starting procedure Stormer predictor summed form systems of ordinary Th)dT tions V^fo V^fs Vf-i Vkfn xn+i