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A pseudospectral method for optimal control based on collocation at the Gauss points
2018 IEEE Conference on Decision and Control (CDC), 2018A Gauss collocation method is developed for solving optimal control problems with convex control constraints. The method has a local exponential convergence rate when the solution of the continuous problem is smooth and the Hamiltonian possesses a convexity property.
William W. Hager +4 more
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Boundary element modeling with variable nodal and collocation point locations
Advances in Engineering Software, 2012In both the real variable and Complex Variable Boundary Element Methods (CVBEM), nodal points are typically located on the problem boundary and then various techniques are used to fit boundary condition values at the nodal point locations such as collocation (equating approximation function to boundary condition values at a discrete set of locations on
T. V. Hromadka II, Devon Zillmer
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Collocation Methods for General Caputo Two-Point Boundary Value Problems
Journal of Scientific Computing, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hui Liang 0001, Martin Stynes
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A new aspect for choosing collocation points for solving biharmonic equations
Applied Mathematics and Computation, 2006The author examines the question of the choice of collocation points for boundary-element methods for the biharmonic equation. He shows that it is possible to choose points in the singular element, so as to minimize the condition number of the corresponding matrix.
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Collocation by the Spline in Tension at Generalized Gaussian Points
1996Summary: We consider the numerical solution for a singularly perturbed two-point boundary value problem: \(\varepsilon y''+cy=f\). To approximate the solution we have used a spline in tension with the continuous first derivative, determined by the collocation at the collocation points which are the generalization of the classical Gaussian points. The B-
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Asymptotic Accuracy and Convergence for Point Collocation Methods
1985Here we continue the asymptotic error analysis of Wendland [118] where we have considered mainly the Galerkin methods. In most of the computer programs, however, the point collocation has been implemented as one of the weighted residual techniques for boundary element methods.
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One-point pseudospectral collocation for the one-dimensional Bratu equation
Applied Mathematics and Computation, 2011The approximate solution of the well-known Bratu problem \[ u_{xx}+\lambda \exp (u) =0, \quad u(\pm 1)=0, \] is revisited. As the first main result, it is shown that over the entire lower branch, and most of the upper branch, the solution is well approximated by a parabola, \(u(x)\approx u_0 (1-x^2)\), where \(u_0\) is determined by collocation at a ...
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On extremal point collocation method for fluid flow problems
Applied Scientific Research, 1962Using Tchebyscheff’s norm a numerical method called “Extremal point collocation method” has been developed for fluid flow problems. The method has been applied to the following problems: 1) flow near a stagnation point; 2) flow near a rotating disk. It has been found that this method gives better results than other approximate methods.
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Collocation Solution for Point-Supported Square Plates
Journal of Applied Mechanics, 1978Rajaiah, K, Rao, AK
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Modelling dissipative silencers using point collocation
2008Dissipative silencers are widely used in ducts to attenuate broad band noise. Silencers may assume many different shapes and sizes, ranging from a relatively compact automotive exhaust silencer, to a much larger HVAC splitter silencer. To accommodate such a wide range of silencer geometries it is convenient to use numerical methods such as the finite ...
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