A Method of Successive Approximations for Computing Combustion Equilibria on a High Speed Digital Computer

1959 ◽  
Vol 63 (4) ◽  
pp. 521-525 ◽  
Author(s):  
D. S. Villars
Keyword(s):  
Digital Computer ◽  
High Speed ◽  
Successive Approximations ◽  
Method Of Successive Approximations

Overview Study of the Analytical Analysis of the Internal Dynamics of Nonlinear Time Heteronymous Planetary Differential Systems

2016 ◽  
Vol 821 ◽  
pp. 213-220
Author(s):  
Milan Hortel ◽  
Alena Škuderová
Keyword(s):  
High Speed ◽  
Wide Spectrum ◽  
Basic Research ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Analytical Analysis ◽  
The Given ◽  
Dynamic Phenomena ◽  
Long Term Studies

The light high-speed transmission systems with minimum dimensions and weights may show a wide spectrum of properties extending from the regular - periodic solutions to irregular ones of chaotic character. The method of transformation of differential boundary value problems to equivalent nonlinear integro-differential equations with solving kernels of Green’s type and the method of successive approximations are applied for analytical analysis of dynamic phenomena. The paper contains the concise summary of the long-term studies in the given area of basic research.

ON A SUCCESSIVE APPROXIMATION METHOD FOR INTERPRETING GRAVITY ANOMALIES

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1215-1228 ◽  
Author(s):  
Z. Frankenberger Danes
Keyword(s):  
Digital Computer ◽  
High Speed ◽  
Gulf Coast ◽  
Gravity Anomalies ◽  
Whole Body ◽  
Successive Approximations ◽  
Successive Approximation Method ◽  
Numerical Work ◽  
Salt Domes ◽  
The Individual

A new method for quantitative interpretation of gravity anomalies is presented. The disturbing body is represented by a finite number of vertical prisms arranged on a pre‐determined, regular grid. The horizontal dimensions of the individual prisms are small enough that they can be approximated by vertical‐line mass elements at the axis of the prisms. Formulas for gravity due to one prism are derived and, for the case of Gulf Coast salt densities, plotted on Figure 1. Gravity due to the whole body is an algebraic sum of the contributions of all prisms at the appropriate depths and distances. This method makes possible the direct interpretation by successive approximations by introducing proper geologic limitations. All the numerical work can be conveniently done on a high‐speed digital computer. The method is especially suitable for features with predominant vertical dimension such as salt domes and igneous plugs. It gives at least the same, and possibly higher, degree of accuracy as the graphical dot chart methods and, carried out on a digital computer, should be about two thousand times faster.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

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