The higher order theory of supercavitating cascades with constant pressure cambered blades
Solution for nonlinear problem supercavitating, constant pressure cambered cascades with finite cavities
Yim, B.↗
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Accelerating the convergence of discretization algorithms.
Convergence of discrete approximations accelerated solutions of nonlinear operator equations in Banach spaces
Pereyra, V.↗
Iteration procedures for indirect trajectory optimization methods.
Numerical method solution of nonlinear two point boundary value problem associated with optimum transfer of spacecraft
Lewallen, J. M.↗
FORTRAN 4 program calculates velocities and streamlines in a tandem blade turbomachine
Computer program gives blade-to-blade solution of the two-dimensional, subsonic, compressible, nonviscous flow problem for a circular or straight infinite cascade of tandem or slotted turbomachine blades. The method of solution is based on the stream function using iterative solution of nonlinear finite-difference equations.
Katsanis, T.↗
Variable mesh methods for differential equations
Variable mesh multistep methods for numerical solution of nonlinear differential equations
Van Wyk, R.↗
Calculation of complex chemical equilibria.
Complex chemical equilibrium calculation, analyzing thermodynamic principles and solution to nonlinear equations
Gordon, S.↗
On the numerical solution of degenerate linear and nonlinear elliptic boundary value problems.
Scheme for choosing approximating system of difference equations for degenerate linear and nonlinear elliptic boundary value problems
Kushner, H. J.↗
Local mapping relations and global implicit function theorems
Nonlinear equation solution based on local mapping relations and global implicit function theorems for Banach space problems
Rheinboldt, W. C.↗
Theoretical investigation on transverse mode combustion instability for liquid propellant rockets
Mathematical solution of nonlinear transverse combustion instability problems in thin annular liquid propellant rocket chambers
Lorenzetto, J. H.↗
Nonlinear programming in design of control systems with specified handling qualities.
A method is described for using nonlinear programing in the computer-aided design of aircraft control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector, and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter aircraft, in which the requirements vector is chosen from the official handling-qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains.
Schy, A. A.↗
Computer-aided design of control systems to meet many requirements
A method is described for using nonlinear programing in the computer-aided design of airplane control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector (instead of attempting to combine them into a single scalar criterion, as is usually done), and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter airplane, in which the requirements vector is chosen from the official handling qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains. The choice of the final design for each case is not unique but depends on the designer's decision as to which achievable set of requirements levels represents the best for that system. Results indicate that it may be possible to design constant parameter SAS which can satisfy the most stringent handling qualities requirements for fighter airplanes in all flight conditions. The role of the designer as a decision maker, interacting with the computer program, is discussed. Advantages of this type of designer-computer interaction are emphasized. Desirable extensions of the method are indicated.
Schy, A. A.↗
A variable step incremental procedure
Description of a variable step incremental procedure for the solution of nonlinear equations in finite element structural analysis. The proposed procedure is effective in improving the accuracy of the basic incremental technique and in providing, in addition, an accurate estimate of the discretization error. The proposed approach is highly appropriate for solving problems for which the user has no a priori estimate of the step size to use.
Thomas, G. R.↗
Compressible seal flow analysis using the finite element method with Galerkin solution technique
A finite element method with a Galerkin solution (FEMGS) technique is formulated for the solution of nonlinear problems in high-pressure compressible seal flow analyses. An example of a three-dimensional axisymmetric flow having nonlinearities, due to compressibility, area expansion, and convective inertia, is used for illustrating the application of the technique.
Zuk, J.↗
The determination of orbits using Picard iteration
The determination of orbits by using Picard iteration is reported. This is a direct extension of the classical method of Picard that has been used in finding approximate solutions of nonlinear differential equations for a variety of problems. The application of the Picard method of successive approximations to the initial value and the two point boundary value problems is given.
Mikkilineni, R. P.↗
A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics
A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.
Martin, E. D.↗
A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics
A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.
Martin, E. D.↗
Varieties of operator manipulation
A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.
Doohovskoy, A.↗
Finite elements and finite differences for transonic flow calculations
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Hafez, M. M.↗