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  • NUMERICAL ANALYSIS  (4)
  • AIRCRAFT PROPULSION AND POWER  (1)
  • 1975-1979  (5)
  • 1
    Publication Date: 2019-06-27
    Description: A study was conducted to determine how errors are propagated when numerical methods are applied to a differential function f(y,t) which is nonlinear in y, with emphasis on stable propagation of the errors.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-157732
    Format: application/pdf
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  • 2
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    In:  Other Sources
    Publication Date: 2019-07-13
    Description: In the present paper, two FORTRAN programs are described which use an interactive graphic terminal to generate accuracy and stability plots for a given multistep integrator of ordinary differential equations (ODE). One program treats the fixed-stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution. It also generates the linear stability region. The other program generates an analog with an accuracy plot. Both systems are capable of computing method coefficients from a simple specification of the method. Example plots are given.
    Keywords: NUMERICAL ANALYSIS
    Type: International Symposium on Simulation Software and Numerical Methods for Differential Equations; Mar 09, 1977 - Mar 11, 1977; Blacksburg, VA
    Format: text
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  • 3
    Publication Date: 2019-06-27
    Description: A local stability analysis is presented for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. It is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and the one-leg k-step numerical solution can be approximated. Attention is given to the example of the two-dimensional problem involving the stability of the longitudinal equations of motion of a gliding jet aircraft.
    Keywords: NUMERICAL ANALYSIS
    Type: Mathematics of Computation; 33; Apr. 197
    Format: text
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  • 4
    Publication Date: 2019-06-27
    Description: A design technique, method and apparatus are delineated for controlling the bypass gas stream pressure and varying the bypass ratio of a mixed flow gas turbine engine in order to achieve improved performance. The disclosed embodiments each include a mixing device for combining the core and bypass gas streams. The variable area mixing device permits the static pressures of the core and bypass streams to be balanced prior to mixing at widely varying bypass stream pressure levels. The mixed flow gas turbine engine therefore operates efficiently over a wide range of bypass ratios and the dynamic pressure of the bypass stream is maintained at a level which will keep the engine inlet airflow matched to an optimum design level throughout a wide range of engine thrust settings.
    Keywords: AIRCRAFT PROPULSION AND POWER
    Format: application/pdf
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  • 5
    Publication Date: 2019-06-27
    Description: The problem of modelling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulae. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulae and two different stepsizes to illustrate the appropriateness of the criteria.
    Keywords: NUMERICAL ANALYSIS
    Type: Applied Mathematical Modelling; 2; June 197
    Format: text
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