## Numerical derivatives and nonlinear analysis |

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### Contents

Methods for Numerical Differentiation | 1 |

Nonlinear Least Squares | 15 |

Optimal Control | 35 |

Copyright | |

5 other sections not shown

### Common terms and phrases

automatic derivative evaluation automatic solution boundary conditions boundary value problem calculation calculus of variations computed cost functional Defines the vector derivative vectors derivatives with respect described in Section differential constraints DIMENSION equa equal to zero Euler-Lagrange equations Euler's method First-Order System Forms the sum Fortran listing Fortran program given in Section given in Table GOSUB Gradient Method grid intervals Hamiltonian function IMPLICIT incremented initial conditions INPUT subroutine integrand IROW linear algebraic main program matrix method of solution Multiplies Newton-Raphson method Newton-Raphson recurrence relation Number of components numerical results numerical solution optimal control problem ordinary differential equations parameters partial derivatives Pontryagin's maximum principle program listing Reference REM CALL RETURN END SUBROUTINE Runge-Kutta integration method Runge-Kutta method scalar second derivatives Second-Order System simplest problem solved Store subroutine INPUT subroutine LIN Sukhanov's method table method tions two-point boundary value variables and vectors vector components vectors corresponding Wengert