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Showing 1 to 19 of 19 for “"Linear algebraic equations"”.
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Exploiting compression in solving discretized linear systems
Solving systems of linear algebraic equations is crucial for many computational problems in science and engineering. Numerous techniques are available for solving such linear systems, including direct methods such as Gaussian elimination and iterative methods such as GMRES. This thesis proposes a …
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Analysis of an oscillating engine for power generation based on the "Drinking Bird Toy"
… head. The mathematical model resulted in seven linear algebraic equations to be solved simultaneously. The iterative nature of the calculations necessitated the use of the University of Missouri at Columbia IBM36O digital computer. The calculations were performed for Freon-11 as internal working …
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Optimal control of a rotating cylinder partially filled with ideal fluid
… to discretize the system and obtain a set of n linear algebraic equations. In both cases the treatment is two dimensional and axial motion of the fluid is considered negligible. In both models, the uncontrolled system, shown by earlier researchers to be inherently unstable, is found to be …
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Numerical solution and spectrum of boundary-domain integral equations
… (BDIE)/ Boundary-Domain Integro-Differential Equations (BDIDEs) and Localized Boundary-Domain Integral Equation (LBDIE)/Localized Boundary-Domain Integro-Differential Equations (LBDIDEs) related to the Neumann and Dirichlet boundary value problem for a scalar elliptic PDE with variable …
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Development and testing of a laboratory digital controller
… to solve some of the tedious and frequent linear algebraic equations involved in MIMO state space analysis of control. These programmes were used extensively during the testing phase of the controller as applied to a multivariable system which was a coupled electric drive. Finally a brief …
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Transonic thermal blooming
According to the linearized solutions for thermal blooming, the density perturbations become infinite (i.e. "catastrophic" defocusing) as the Mach number approaches unity. However, the nonlinearities in the transonic equations cutoff the trend to infinity, and the values of the flow perturbation …
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Plastic buckling of initially imperfect stiffened cylinders in axial compression
… principle of virtual work to obtain a set of non-linear algebraic equations whose solution provides complete information about the prebuckling equilibrium path. Bifurcation from the primary path is examined by making use of a functional whose first variation is zero when two solutions to the …
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Noniterative construction of optimal quadratically-nonlinear ODE models from time series
… the problem of constructing a quadratically nonlinear ordinary differential equation (ODE) system from time series, with the latter obtained either from experiment, or from computational simulation using a higher-dimensional mathematical model (e.g., one or more partial differential equations). …
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An investigation into direct sparse matrix solution schemes in the finite element method
… involves the solution of large systems of sparse linear algebraic equations. The solution of these systems often represents a significant or even dominant component of the total solution time. Various sparse matrix techniques and strategies have been developed to reduce the time and cost of …
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New symmetries from old: exploiting lie algebra structure to determine infinitesimal symmetries of differential equations
… known Lie symmetries of a system of differential equations to help find more symmetries of the system. A Lie (or infinitesimal) symmetry of a system of differential equations is a transformation of its dependent and independent variables, depending on continuous parameters, which maps any solution …
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ΛΥΣΕΙΣ ΙΣΟΡΡΟΠΙΑΣ ΚΑΙ ΕΥΣΤΑΘΕΙΑ ΣΕ ΤΡΟΧΙΕΣ ΑΣΤΕΡΟΕΙΔΩΝ ΥΠΟ ΤΗΝ ΕΠΙΔΡΑΣΗ ΑΙΩΝΙΩΝ ΠΑΡΕΛΞΕΩΝ
… THE A-H PLANE, AS ROOTS OF A SYSTEM OF TWO NON- LINEAR ALGEBRAIC EQUATIONS. WE THEN DISTINGUISH THE "ACCEPTABLE EQUILIBRIUM SOLUTIONS", (AES). NEXT, WE STUDY THE STABILITY OF THE AES. THE STABILITY ANALYSIS REQUIRED FOR THE HIGHER ORDER TERMS OF OUR EQUATIONS SEEMS TO PRESENT GREAT DIFFICULTIES …
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ΔΙΦΑΣΙΚΗ ΡΟΗ ΑΕΡΑ - ΣΤΕΡΕΩΝ ΣΩΜΑΤΙΔΙΩΝ ΣΕ ΚΛΕΙΣΤΟΥΣ ΑΓΩΓΟΥΣ
… HORIZONTAL PIPES IS EXAMINED. IN DERIVING THE EQUATIONS, IT IS ASSUMED THAT A GAS PARTICLE SUSPENSION MAYBE REGARDED AS A CONTINUUM, I.E. THE PARTICLES ARE CONSIDERED TO BE CONTINUOUSLY, BUT NOT NECESSARILY UNIFORMLY, DISTRIBUTED THROUGHOUT THE GAS. THE FUNDAMENTAL EQUATIONS OF THE TWO-PHASE …
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Thermal stresses in a finite solid-propellant grain
… presented are significant since the simultaneous linear algebraic equations, for the arbitrary constants, are easily solved. It is true that, in principle, an infinite number of these arbitrary constants must be determined. From a practical point of view, however, the arbitrary constants can …
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A methodology for non-Intrusive projection-based model reduction of expensive black-box PDE-based systems and application in the many-query context
… access to the discrete form of governing equations of the high-fidelity model. The projection is commonly done on a subspace determined via POD. However when commercial codes are used as the high-fidelity model, such an approach is not possible in general. Usually in such circumstances, a …
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Actuator Disk Theory for Compressible Flow
… test flights. The compressible-flow governing equations were applied to a propeller and a turbine for both the bare and ducted cases. The solutions to the resulting system of coupled, non-linear, algebraic equations were obtained using an iterative approach. The results showed that the power …
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The approximate determinantal assignment problem
… Problem (DAP) is one of the central problems of Algebraic Control Theory and refers to solving a system of non-linear algebraic equations to place the critical frequencies of the system to specied locations. This problem is decomposed into a linear and a multi-linear subproblem and the …
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Development of a Global/Local Approach and a Geometrically Non-linear Local Panel Analysis for Structural Design
… analysis capability for the geometrically non-linear response of compressively loaded prismatic plate structures was developed. Both a "full" finite strip solution procedure and a "reduced" solution procedure were implemented in a FORTRAN 90 computer code, and comparisons were made with results …
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The numerical modelling of composite floors exposed to fire
… governing differential equation into a system of linear algebraic equations. To calculate the plate rigidities, it is necessary to find curvatures for all mesh points in the two planes using finite difference operators. The thermal strains , are superimposed, on the mechanical strains associated …
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Výpočet algebraických rovnic
Práce se zabývá řešením soustav lineárních algebraických rovnic metodou převodu na soustavu rovnic diferenciálních, ukáže ale i jiné známější metody. V teoretické části popisuje matematické operace s maticemi. V práci jsou pomocí programů Matlab a TKSL vyřešeny příklady a porovnány jejich hodnoty …