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Showing 1 to 20 of 36 for “"Nonlinear Differential Equations"”.
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Theoretical Analysis of Nonlinear Differential Equations
<p>Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, …
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Functional analysis of systems characterized by nonlinear differential equations.
Massachusetts Institute of Technology. Dept. of Electrical Engineering. Thesis. 1966. Ph.D.
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A Variation of the Carleman Embedding Method for Second Order Systems.
… us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for higher order nonlinear ordinary differential …
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Solving the Differential Equation for the Probit Function Using a Variant of the Carleman Embedding Technique.
… first order and, less efficiently, second order nonlinear differential equations. In this thesis, we show that solutions to the second order nonlinear differential equation for the probit function can be approximated efficiently using a variant of the Carleman embedding technique.</p>
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Bending of an Axially Loaded Strand With Friction and the Mechanics of Wire Rope Reinforced Cylinders
… for equilibrium are obtained by solving the six nonlinear, differential equations of equilibrium of a thin wire. The stresses due to bending are then superimposed on the stresses in the wires due to the axial loading.
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The Effects of Fixed Factors of Production in Optimal Growth Models
… do so involves solving an unsolvable series of nonlinear differential equations.
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Second-Order Relative Motion Equations
… solution of second order relative motion equations. The equations of motion for a Keplerian orbit in spherical coordinates are expanded in Taylor series form using reference conditions consistent with that of a circular orbit. Only terms that are linear or quadratic in state variables are …
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Action Potential Simulation of the Hirudo Medicinalis's Retzius Cell in MATLAB
… and Huxley’s experimentally derived set of nonlinear differential equations was implemented to accurately simulate the action potential of the <em>Hirudo Medicinalis’s</em> Retzius cell in <em>MATLAB</em> under analogous conditions to those found in the Retzius cell environment. The …
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Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems
<p>In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It …
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Influence of extreme velocities on dynamic cavity expansion
… is considered under extreme velocities. Two nonlinear differential equations are used to describe the steady-state expansion. Using numerical integration, this system is solved to explore the behavior under extreme expansion velocities. By gradually increasing the expansion velocities, we …
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Compact modeling of circuits and devices in Verilog-A
… a circuit or device is a system of linear and/or nonlinear differential equations that effectively models the behavior of the circuit or device. Compact modeling plays a critical role in circuit simulation, because in order to simulate a circuit with a specific component, the compact model of this …
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A new first order solution to the relative motion problem with applications to intercept and rendezvous
… of the variables which occur in the differential equations of relative motion. The results of this analysis are compared with other first order solutions and with complete solutions obtained by numerically integrating the exact, nonlinear differential equations of motion. It was found …
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Advances in numerical bifurcation software : MatCont
… dynamical systems this means that it considers nonlinear differential equations without any special form and without restrictions except for differentiability up to a sufficiently high order (in the present state of MatCont never higher than five.) The number of equations is not fixed in advance …
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Taming of Complex Dynamical Systems
… and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D …
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Adapting the Standard SIR Disease Model in Order to Track and Predict the Spreading of the EBOLA Virus Using Twitter Data
… of social users in a fashion similar to nonlinear wave propagation- like a shock wave, visualized as a spike in Tweet activity. The spreading was modeled as a system isomorphic to a modified SIR (Susceptible, Infected, Removed disease model) system of three coupled nonlinear differential …
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Mathematical Simulation of Direct Glucose Fuel Cell
… two sets (for anode and cathode) of first order nonlinear differential equations (derived from conservation equations) valid for heterogeneous domain consisting of electrodes, gas diffusion layers, anion exchange membrane, catalyst layers and flow channels. These equations were solved using …
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A Legendre Pseudospectral Method for rapid optimization of launch vehicle trajectories
… differentiation matrix to discretize nonlinear differential equations (such as the equations of motion) into nonlinear algebraic equations. The equations are then posed in the form of a nonlinear optimization problem and solved numerically. The method is demonstrated to work very well …
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A nonlinear dynamic system for spread spectrum code acquisition
Nonlinear differential equations and iterated maps can perform any computation. Sometimes, the most difficult part of performing a useful computation, however, is writing the program. Furthermore, in practice, we often need to build special purpose computing hardware suited to run a particular …
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Global dynamic optimization
… Furthermore, I show that the solution of the differential equations is affine in the parameters. Because the feasible set is convex pointwise in time, the standard result that a convex function composed with an affine function remains convex yields the desired result that the integrand is …
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Temperature control strategies for radiant floor heating systems
… enclosure. The overall model was described by nonlinear differential equations, which were solved using finite numerical methods. The predicted responses from the model were compared with published experimental data. The comparisons were made covering a wide range of weather and operating …
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