Convolution Type Operators with Symbols Generated by Slowly Oscillating and Piecewise Continuous Matrix Functions

The paper considers a method for simulating the flight of a multistage rocket in Matlab using Simulink software for control and guidance. The model takes into account the anisotropy of the gravity of the Earth, changes in the pressure and density of the atmosphere, piecewise continuous change of the center of mass and the moment of inertia of the rocket during the flight. Also, the proposed model allows you to work out various targeting options using both onboard and ground‑based information tools, to load information from the ground‑based radar, with imitation of «non‑ideality» of incoming target designations as a result of changes in the accuracy of determining coordinates and speeds, as well as signal fluctuations. It is stipulated that the design is variable not only by the number of steps, but also by their types. The calculations are implemented in a matrix form, which allows parallel operations in each step of processing a multidimensional state vector of the simulated object.

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Multi-stage linear Gauss pseudospectral method for piecewise continuous nonlinear optimal control problems

IEEE Transactions on Aerospace and Electronic Systems ◽

10.1109/taes.2021.3054074 ◽

2021 ◽

pp. 1-1

Author(s):

Yang Li ◽

Wanchun Chen ◽

Liang Yang

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Pseudospectral Method ◽

Nonlinear Optimal Control ◽

Control Problems ◽

Multi Stage ◽

Gauss Pseudospectral Method ◽

Piecewise Continuous

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A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

Advances in Computational Mathematics ◽

10.1007/s10444-021-09866-7 ◽

2021 ◽

Vol 47 (3) ◽

Author(s):

Timon S. Gutleb

Keyword(s):

Open Source ◽

Spectral Method ◽

Jacobi Polynomial ◽

Numerical Experiments ◽

Exponential Convergence ◽

Analytic Solutions ◽

Convolution Type ◽

Volterra Equations ◽

Polynomial Bases ◽

Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

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The Calderón–Zygmund Theorem with an $$L^1$$ Mean Hörmander Condition

Journal of Fourier Analysis and Applications ◽

10.1007/s00041-021-09810-9 ◽

2021 ◽

Vol 27 (2) ◽

Author(s):

Soichiro Suzuki

Keyword(s):

Singular Integral ◽

Integral Operators ◽

Acta Math ◽

Limited Range ◽

Singular Integral Operators ◽

Convolution Type ◽

Worst Case ◽

Hörmander Condition

AbstractIn 2019, Grafakos and Stockdale introduced an $$L^q$$ L q mean Hörmander condition and proved a “limited-range” Calderón–Zygmund theorem. Comparing their theorem with the classical one, it requires weaker assumptions and implies the $$L^p$$ L p boundedness for the “limited-range” instead of $$1< p < \infty $$ 1 < p < ∞ . However, in this paper, we show that the $$L^q$$ L q mean Hörmander condition is actually enough to obtain the $$L^p$$ L p boundedness for all $$1< p < \infty $$ 1 < p < ∞ even in the worst case $$q=1$$ q = 1 . We use a similar method to that used by Fefferman (Acta Math 124:9–36, 1970): form the Calderón–Zygmund decomposition with the bounded overlap property and approximate the bad part. Also we give a criterion of the $$L^2$$ L 2 boundedness for convolution type singular integral operators under the $$L^1$$ L 1 mean Hörmander condition.

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