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Статті в журналах з теми "Diagonal hyperbolic systems"

Автор: Grafiati

Опубліковано: 17 серпня 2022

Оновлено: 16 вересня 2022

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1

EL HAJJ, AHMAD, and RÉGIS MONNEAU. "GLOBAL CONTINUOUS SOLUTIONS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA." Journal of Hyperbolic Differential Equations 07, no. 01 (March 2010): 139–64. http://dx.doi.org/10.1142/s0219891610002050.

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Анотація:

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonal hyperbolic system appears naturally in the modeling of the dynamics of dislocation densities.

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2

EL HAJJ, AHMAD, and RÉGIS MONNEAU. "UNIQUENESS RESULTS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA." Journal of Hyperbolic Differential Equations 10, no. 03 (September 2013): 461–94. http://dx.doi.org/10.1142/s0219891613500161.

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We study the uniqueness of solutions to diagonal hyperbolic systems in one spatial dimension and we present two uniqueness results. First, we establish a global existence and uniqueness theorem for continuous solutions to strictly hyperbolic systems. Second, we establish a global existence and uniqueness theorem for Lipschitz continuous solutions to hyperbolic systems that need not be strictly hyperbolic. Furthermore, an application is presented for one-dimensional flows in isentropic gas dynamics.

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3

Colombini, Ferruccio, and Daniele Del Santo. "Blow-up for hyperbolic systems in diagonal form." Nonlinear Differential Equations and Applications 8, no. 4 (November 2001): 465–72. http://dx.doi.org/10.1007/pl00001458.

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4

Spehner, D. "Spectral form factor of hyperbolic systems: leading off-diagonal approximation." Journal of Physics A: Mathematical and General 36, no. 26 (June 17, 2003): 7269–90. http://dx.doi.org/10.1088/0305-4470/36/26/304.

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5

Jourdain, Benjamin, and Julien Reygner. "A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data." Journal of Hyperbolic Differential Equations 13, no. 03 (September 2016): 441–602. http://dx.doi.org/10.1142/s0219891616500144.

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Анотація:

This paper is devoted to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions or, more generally, nonconstant monotonic bounded functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic fields, we construct a multi-type version of the sticky particle dynamics and we obtain the existence of global weak solutions via a compactness argument. We then derive a [Formula: see text] stability estimate on the particle system which is uniform in the number of particles. This allows us to construct nonlinear semigroups solving the system in the sense of Bianchini and Bressan [Vanishing viscosity solutions of nonlinear hyperbolic systems, Ann. of Math. (2) 161(1) (2005) 223–342]. We also obtain that these semigroup solutions satisfy a stability estimate in Wasserstein distances of all order, which extends the classical [Formula: see text] estimate and generalizes to diagonal systems a result by Bolley, Brenier and Loeper [Contractive metrics for scalar conservation laws, J. Hyperbolic Differ. Equ. 2(1) (2005) 91–107] in the scalar case. Our results are established without any smallness assumption on the variation of the data, and we only require the characteristic fields to be Lipschitz continuous and the system to be uniformly strictly hyperbolic.

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6

Li, Ta-Tsien, and Yue-Jun Peng. "Cauchy problem for weakly linearly degenerate hyperbolic systems in diagonal form." Nonlinear Analysis: Theory, Methods & Applications 55, no. 7-8 (December 2003): 937–49. http://dx.doi.org/10.1016/j.na.2003.08.010.

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7

Dus, Mathias, Francesco Ferrante, and Christophe Prieur. "On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 23. http://dx.doi.org/10.1051/cocv/2019069.

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Анотація:

This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.

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8

OHWA, HIROKI. "THE SHOCK CURVE APPROACH TO THE RIEMANN PROBLEM FOR 2 × 2 HYPERBOLIC SYSTEMS OF CONSERVATION LAWS." Journal of Hyperbolic Differential Equations 07, no. 02 (June 2010): 339–64. http://dx.doi.org/10.1142/s0219891610002128.

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We consider the Riemann problem for 2 × 2 hyperbolic systems of conservation laws in one space variable. Our main assumptions are that the product of non-diagonal elements within the Fréchet derivative (Jacobian) of the flux is positive, and that the system is genuinely nonlinear. The first assumption implies that the system is strictly hyperbolic, but we do not require a convexity-like condition such as the Smoller–Johnson condition. By using the shock curve approach, we show that those two assumptions are sufficient to establish the uniqueness of self-similar solutions satisfying the Lax entropy conditions at discontinuities.

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9

Li, Tatsien, and Zhiqiang Wang. "Global exact boundary controllability for first order quasilinear hyperbolic systems of diagonal form." International Journal of Dynamical Systems and Differential Equations 1, no. 1 (2007): 12. http://dx.doi.org/10.1504/ijdsde.2007.013741.

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10

Yu, Lixin. "Global exact boundary observability for first-order quasilinear hyperbolic systems of diagonal form." Mathematical Methods in the Applied Sciences 35, no. 13 (June 22, 2012): 1505–17. http://dx.doi.org/10.1002/mma.2520.

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11

Sieber, Martin. "Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems." Journal of Physics A: Mathematical and General 35, no. 42 (October 8, 2002): L613—L619. http://dx.doi.org/10.1088/0305-4470/35/42/104.

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12

Passler, Nikolai C., Xiang Ni, Guangwei Hu, Joseph R. Matson, Giulia Carini, Martin Wolf, Mathias Schubert, et al. "Hyperbolic shear polaritons in low-symmetry crystals." Nature 602, no. 7898 (February 23, 2022): 595–600. http://dx.doi.org/10.1038/s41586-021-04328-y.

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AbstractThe lattice symmetry of a crystal is one of the most important factors in determining its physical properties. Particularly, low-symmetry crystals offer powerful opportunities to control light propagation, polarization and phase1–4. Materials featuring extreme optical anisotropy can support a hyperbolic response, enabling coupled light–matter interactions, also known as polaritons, with highly directional propagation and compression of light to deeply sub-wavelength scales5. Here we show that monoclinic crystals can support hyperbolic shear polaritons, a new polariton class arising in the mid-infrared to far-infrared due to shear phenomena in the dielectric response. This feature emerges in materials in which the dielectric tensor cannot be diagonalized, that is, in low-symmetry monoclinic and triclinic crystals in which several oscillators with non-orthogonal relative orientations contribute to the optical response6,7. Hyperbolic shear polaritons complement previous observations of hyperbolic phonon polaritons in orthorhombic1,3,4 and hexagonal8,9 crystal systems, unveiling new features, such as the continuous evolution of their propagation direction with frequency, tilted wavefronts and asymmetric responses. The interplay between diagonal loss and off-diagonal shear phenomena in the dielectric response of these materials has implications for new forms of non-Hermitian and topological photonic states. We anticipate that our results will motivate new directions for polariton physics in low-symmetry materials, which include geological minerals10, many common oxides11 and organic crystals12, greatly expanding the material base and extending design opportunities for compact photonic devices.

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13

Wang, Zhiqiang. "Global exact controllability for quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics." Nonlinear Analysis: Theory, Methods & Applications 69, no. 2 (July 2008): 510–22. http://dx.doi.org/10.1016/j.na.2007.05.037.

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14

Monasse, L., and R. Monneau. "Gradient Entropy Estimate and Convergence of a Semi-Explicit Scheme for Diagonal Hyperbolic Systems." SIAM Journal on Numerical Analysis 52, no. 6 (January 2014): 2792–814. http://dx.doi.org/10.1137/130950458.

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15

Demengel, F., and J. Rauch. "Measure valued solutions of asymptotically homogeneous semilinear hyperbolic systems in one space variable." Proceedings of the Edinburgh Mathematical Society 33, no. 3 (October 1990): 443–60. http://dx.doi.org/10.1017/s0013091500004855.

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Анотація:

We study systems which in characteristic coordinates have the formwhere A is a k × k diagonal matrix with distinct real eigenvalues. The nonlinearity F is assumed to be asymptotically homogeneous in the sense, that it is a sum of two terms, one positively homogeneous of degree one in u and a second which is sublinear in u and vanishes when u = 0. In this case, F(t, x, u(t)) is meaningful provided that u(t) is a Radon measure, and, for Radon measure initial data there is a unique solution (Theorem 2.1).The main result asserts that if μn is a sequence of initial data such that, in characteristic coordinates, the positive and negative parts of each component, , converge weakly to μ±, then the solutions coverge weakly and the limit has an interesting description given by a nonlinear superposition principle.Simple weak converge of the initial data does not imply weak convergence of the solutions.

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16

Fusco, Giorgio, and Waldyr Muniz Oliva. "Jacobi matrices and transversality." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 109, no. 3-4 (January 1988): 231–43. http://dx.doi.org/10.1017/s0308210500027748.

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SynopsisThe paper deals with smooth nonlinear ODE systems in ℝn, ẋ = f(x), such that the derivative f′(x) has a matrix representation of Jacobi type (not necessarily symmetric) with positive off diagonal entries. A discrete functional is introduced and is discovered to be nonincreasing along the solutions of the associated linear variational system ẏ = f′(x(t))y. Two families of transversal cones invariant under the flow of that linear system allow us to prove transversality between the stable and unstable manifolds of any two hyperbolic critical points of the given nonlinear system; it is also proved that the nonwandering points are critical points. A new class of Morse–Smale systems in ℝn is then explicitly constructed.

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17

BOUCHUT, FRANÇOIS. "A REDUCED STABILITY CONDITION FOR NONLINEAR RELAXATION TO CONSERVATION LAWS." Journal of Hyperbolic Differential Equations 01, no. 01 (March 2004): 149–70. http://dx.doi.org/10.1142/s0219891604000020.

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We consider multidimensional hyperbolic systems of conservation laws with relaxation, together with their associated limit systems. A strong stability condition for such asymptotics has been introduced by Chen, Levermore and Liu, namely the existence of an entropy extension. We propose here a new stability condition, the reduced stability condition, which is weaker than the previous one, but still has the property to imply the subcharacteristic or interlacing conditions, and the dissipativity of the leading term in the Chapman–Enskog expansion. This reduced stability condition has the advantage of involving only the submanifold of equilibria, or maxwellians, so that it is much easier to check than the entropy extension condition. Our condition generalizes the one introduced by the author in the case of kinetic, i.e. diagonal semilinear relaxation. We provide an adapted stability analysis in the context of approximate Riemann solvers obtained via relaxation systems.

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18

Shao, Zhi-Qiang. "Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems of diagonal form with large BV data." Communications on Pure & Applied Analysis 12, no. 6 (2013): 2739–52. http://dx.doi.org/10.3934/cpaa.2013.12.2739.

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19

Reygner, Julien, and Benjamin Jourdain. "Optimal convergence rate of the multitype sticky particle approximation of one-dimensional diagonal hyperbolic systems with monotonic initial data." Discrete and Continuous Dynamical Systems 36, no. 9 (May 2016): 4963–96. http://dx.doi.org/10.3934/dcds.2016015.

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20

Zheng, Yongshu, and Fagui Liu. "A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM." Acta Mathematica Scientia 20, no. 4 (January 2000): 571–76. http://dx.doi.org/10.1016/s0252-9602(17)30669-0.

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21

Shao, Zhi-Qiang. "Global existence of classical solutions to the mixed initial–boundary value problem for quasilinear hyperbolic systems of diagonal form with large BV data." Journal of Mathematical Analysis and Applications 360, no. 2 (December 2009): 398–411. http://dx.doi.org/10.1016/j.jmaa.2009.06.066.

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22

Montoya, Oscar Danilo, Alexander Molina-Cabrera, and Jesus C. Hernández. "A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation." Electronics 10, no. 21 (October 21, 2021): 2573. http://dx.doi.org/10.3390/electronics10212573.

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This paper presents a comparative analysis of six different iterative power flow methods applied to AC distribution networks, which have been recently reported in the scientific literature. These power flow methods are (i) successive approximations, (ii) matricial backward/forward method, (iii) triangular-based approach, (iv) product linearization method, (v) hyperbolic linearization method, and (vi) diagonal approximation method. The first three methods and the last one are formulated without recurring derivatives, and they can be directly formulated in the complex domain; the fourth and fifth methods are based on the linear approximation of the power balance equations that are also formulated in the complex domain. The numerical comparison involves three main aspects: the convergence rate, processing time, and the number of iterations calculated using the classical Newton–Raphson method as the reference case. Numerical results from two test feeders composed of 34 and 85 nodes demonstrate that the derivative-free methods have linear convergence, and the methods that use derivatives in their formulation have quadratic convergence.

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23

Chabchoub, Amin, Kento Mozumi, Norbert Hoffmann, Alexander V. Babanin, Alessandro Toffoli, James N. Steer, Ton S. van den Bremer, Nail Akhmediev, Miguel Onorato, and Takuji Waseda. "Directional soliton and breather beams." Proceedings of the National Academy of Sciences 116, no. 20 (April 26, 2019): 9759–63. http://dx.doi.org/10.1073/pnas.1821970116.

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Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose–Einstein condensates, solids, plasma, hydrodynamics, and optics.

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24

Duan, Ruirui, Junmin Li, Yanni Zhang, Ying Yang, and Guopei Chen. "Stability analysis and H∞ control of discrete T–S fuzzy hyperbolic systems." International Journal of Applied Mathematics and Computer Science 26, no. 1 (March 1, 2016): 133–45. http://dx.doi.org/10.1515/amcs-2016-0009.

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Abstract This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T–S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T–S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T–S fuzzy hyperbolic model with the discrete T–S fuzzy linear one are also given to illustrate the advantage of our approach.

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25

EL HAJJ, Ahmad, Rachida Boudjerada, and Aya Oussayli. "Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems." ESAIM: Mathematical Modelling and Numerical Analysis, July 21, 2020. http://dx.doi.org/10.1051/m2an/2020049.

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In this paper, we consider diagonal non-conservative hyperbolic systems in one space dimension with monotone and large Lipschitz continuous data. Under a certain nonnegativity condition on the Jacobian matrix of the velocity of the system, global existence and uniqueness results of a Lipschitz solution for this system, which is not necessarily strictly hyperbolic, was already proven. We propose a natural implicit scheme satisfiying a similar Lipschitz estimate at the discrete level. This property allows us to prove the convergence of the scheme without assuming it strictly hyperbolic.

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26

Ashok, Sujay K., and Jan Troost. "Path integrals on sl(2,R) orbits." Journal of Physics A: Mathematical and Theoretical, July 11, 2022. http://dx.doi.org/10.1088/1751-8121/ac802c.

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Abstract We quantise orbits of the adjoint group action on elements of the sl(2, ℝ) Lie algebra. The path integration along elliptic slices is akin to the coadjoint orbit quantization of compact Lie groups, and the calculation of the characters of elliptic group elements proceeds along the same lines as in compact groups. The computation of the trace of hyperbolic group elements in a diagonal basis as well as the calculation of the full group action on a hyperbolic basis requires considerably more technique. We determine the action of hyperbolic one-parameter subgroups of PSL(2, ℝ) on the adjoint orbits and discuss global subtleties in choices of adapted coordinate systems. Using the hyperbolic slicing of orbits, we describe the quantum mechanics of an irreducible sl(2, ℝ) representation in a hyperbolic basis and relate the basis to the mathematics of the Mellin integral transform. We moreover discuss the representation theory of the double cover SL(2, ℝ) of PSL(2, ℝ) as well as that of its universal cover. Traces in the representations of these groups for both elliptic and hyperbolic elements are computed. Finally, we motivate our treatment of this elementary quantization problem by indicating applications.

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27

Gugat, Martin, and Jan Giesselmann. "Boundary feedback stabilization of a semilinear model for the flow in star-shaped gas networks." ESAIM: Control, Optimisation and Calculus of Variations, June 7, 2021. http://dx.doi.org/10.1051/cocv/2021061.

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The flow of gas through a pipeline network can be modelled by a coupled system of 1-d quasilinear hyperbolic equations. Often for the solution of control problems it is convenient to replace the quasilinear model by a simpler semilinear model. We analyze the behavior of such a semilinear model on a star-shaped network. The model is derived from the diagonal form of the quasilinear model by replacing the eigenvalues by the sound speed multiplied by 1 or -1 respectively, thus neglecting the influence of the gas velocity which is justified in the applications since it is much smaller than the sound speed. For a star-shaped network of pipes we present boundary feedback laws that stabilize the system state exponentially fast to a position of rest for sufficiently small initial data. We show the exponential decay of the $L^2$-norm for arbitrarily long pipes. This is remarkable since in general even for linear systems, for certain source terms the system can become exponentially unstable if the space interval is too long. Our proofs are based upon an observability inequality and suitably chosen Lyapunov functions. Numerical examples including a comparison of the semilinear and the quasilinear model are presented.

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28

Puppo, G., M. Semplice, and G. Visconti. "Quinpi: Integrating Conservation Laws with CWENO Implicit Methods." Communications on Applied Mathematics and Computation, February 9, 2022. http://dx.doi.org/10.1007/s42967-021-00171-0.

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AbstractMany interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration is quite straightforward for first-order schemes. High order schemes instead also need to control spurious oscillations, which requires limiting in space and time also in the linear case. We propose a framework to simplify considerably the application of high order non-oscillatory schemes through the introduction of a low order implicit predictor, which is used both to set up the nonlinear weights of a standard high order space reconstruction, and to achieve limiting in time. In this preliminary work, we concentrate on the case of a third-order scheme, based on diagonally implicit Runge Kutta ($$\mathsf {DIRK}$$ DIRK ) integration in time and central weighted essentially non-oscillatory ($$\mathsf {CWENO}$$ CWENO ) reconstruction in space. The numerical tests involve linear and nonlinear scalar conservation laws.

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