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Showing 1 to 5 of 5 for “"second order PDE"”.
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A factorization approach for solving the Hamilton-Jacobi equations in nonlinear optimal control
… elementary solutions are then presented. The second approach involves converting the first-order HJ partial differential equation (PDE) to a second-order PDE. Then using a suitable parameterization, this second-order PDE is converted to a coupled system of higher-order nonlinear PDEs which can …
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Similarity Solutions for the Two-Dimensional Diffusion–Advection Equation in Sharp-Corner Geometries
… reducing the equation to a time-independent second-order PDE. By modifying the ansatz, the problem can be recast as an eigenvalue problem. Exploiting elliptic regularity and the strong maximum principle, we invoke the Krein-Rutman theorem to establish the existence and domain-size …
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Continuum Sensitivity Method for Nonlinear Dynamic Aeroelasticity
… of linear partial<br />differential equations (PDEs) obtained by differentiating the original governing equations of<br />the physical system. The linear CSEs may be solved by using the same numerical method<br />used for the original analysis problem. The material (total) derivative, the local …
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SOLVING THE CABLE EQUATION, A SECOND-ORDER TIME DEPENDENT PDE FOR NON-IDEAL CABLES WITH ACTION POTENTIALS IN THE MAMMALIAN BRAIN USING KSS METHODS
… interest to generalize the application of the PDEs including and other than Cable Equation to the study of Neurodegenerative diseases like multiple sclerosis, Alzheimer’s, Parkinsons etc. The ultimate goal would be to be able to study a broad application of numerical methods to understand …
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Dynamical Reduced-Order Models for High-Dimensional Systems
… same: high dimensionality. The goal of reduced-order modeling is to reduce the number of unknowns in a system while minimizing the loss of accuracy in the approximate solution. Ideal model-order reduction techniques are optimal compromises between computational tractability and solution …