Found 103 Documents (Results 1–100)
A class of polynomial approximation methods to second-order delay differential equations. (English) Zbl 07890916
A generalized energy and quadratic invariant preserving (GEQUIP) method for Hamiltonian systems with multiple invariants. (English) Zbl 07890915
Fully decoupled and high-order linearly implicit energy-preserving RK-GSAV methods for the coupled nonlinear wave equation. (English) Zbl 1541.65068
Recent advances in the numerical solution of the nonlinear Schrödinger equation. (English) Zbl 07866531
MSC:
65Mxx
A spectrally accurate step-by-step method for the numerical solution of fractional differential equations. (English) Zbl 1537.65080
Strong backward error analysis of symplectic integrators for stochastic Hamiltonian systems. (English) Zbl 07834031
A fourth-order energy-preserving and symmetric average vector field integrator with low regularity assumption. (English) Zbl 07829074
MSC:
65Mxx
Energy dissipation-preserving GSAV-Fourier-Galerkin spectral schemes for space-fractional nonlinear wave equations in multiple dimensions. (English) Zbl 1529.65012
Arbitrarily high-order accurate and energy-stable schemes for solving the conservative Allen-Cahn equation. (English) Zbl 1533.65194
Relaxation exponential Rosenbrock-type methods for oscillatory Hamiltonian systems. (English) Zbl 1537.65194
Reviewer: Jean-François Coulombel (Toulouse)
Arbitrary high-order structure-preserving methods for the quantum Zakharov system. (English) Zbl 07773314
On convergence of a novel linear conservative scheme for the two-dimensional fractional nonlinear Schrödinger equation with wave operator. (English) Zbl 1538.65417
(Spectral) Chebyshev collocation methods for solving differential equations. (English) Zbl 1523.65100
High-order Runge-Kutta structure-preserving methods for the coupled nonlinear Schrödinger-KdV equations. (English) Zbl 1540.65528
Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation. (English) Zbl 07701112
Conservative finite difference methods for the Boussinesq paradigm equation. (English) Zbl 1540.65341
Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations. (English) Zbl 1534.65202
Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equations. (English) Zbl 1512.65187
Reviewer: Qifeng Zhang (Hangzhou)
A new thermodynamically compatible finite volume scheme for magnetohydrodynamics. (English) Zbl 07670867
Two novel classes of arbitrary high-order structure-preserving algorithms for canonical Hamiltonian systems. (English) Zbl 1515.65311
An arbitrarily high-order energy-preserving scheme for the Lorentz force system. (English) Zbl 1538.65194
Linearly implicit and high-order energy-preserving relaxation schemes for highly oscillatory Hamiltonian systems. (English) Zbl 07652817
A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics. (English) Zbl 1510.76098
A new family of thermodynamically compatible discontinuous Galerkin methods for continuum mechanics and turbulent shallow water flows. (English) Zbl 1503.65223
MSC:
65M60
65L06
65N30
65M12
76F10
76B15
76D05
76N06
76M10
74B20
74S05
80A19
35L02
35Q31
35Q30
35Q79
A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials. (English) Zbl 1500.65007
A novel class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation. (English) Zbl 1513.65402
On thermodynamically compatible finite volume schemes for continuum mechanics. (English) Zbl 07556268
Efficient energy-preserving exponential integrators for multi-component Hamiltonian systems. (English) Zbl 1492.65349
Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function. (English) Zbl 1491.65062
A dissipation-preserving integrator for damped oscillatory Hamiltonian systems. (English) Zbl 1499.65294
Energy-preserving continuous-stage exponential Runge-Kutta integrators for efficiently solving Hamiltonian systems. (English) Zbl 1492.65188
A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles. (English) Zbl 1491.49037
Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation. (English) Zbl 1487.65166
Reviewer: Weizhong Dai (Ruston)
The exponential invariant energy quadratization approach for general multi-symplectic Hamiltonian PDEs. (English) Zbl 1480.65365
High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation. (English) Zbl 1481.65134
Variational integrators for forced Lagrangian systems based on the local path fitting technique. (English) Zbl 1510.70041
Efficient energy preserving Galerkin-Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator. (English) Zbl 1484.65223
Arbitrarily high-order structure-preserving schemes for the Gross-Pitaevskii equation with angular momentum rotation. (English) Zbl 07690841
Two linearly implicit energy preserving exponential scalar auxiliary variable approaches for multi-dimensional fractional nonlinear Schrödinger equations. (English) Zbl 1524.65351
Structure preserving – field directional splitting difference methods for nonlinear Schrödinger systems. (English) Zbl 1496.65101
A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting. (English) Zbl 1482.65227
On convergence of a structure preserving difference scheme for two-dimensional space-fractional nonlinear Schrödinger equation and its fast implementation. (English) Zbl 1524.65352
Linear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov system. (English) Zbl 1476.65196
An integral evolution formula of boundary value problem for wave equations. (English) Zbl 1524.35528
Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations. (English) Zbl 1456.65090
Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations. (English) Zbl 07506165
The time high-order energy-preserving schemes for the nonlocal Benjamin-Ono equation. (English) Zbl 1488.65369
Modified averaged vector field methods preserving multiple invariants for conservative stochastic differential equations. (English) Zbl 1469.65027
Efficient linear energy dissipative difference schemes for the coupled nonlinear damped space fractional wave equations. (English) Zbl 1450.35018
Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping. (English) Zbl 1446.65080
Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles. (English) Zbl 1477.65265
Reviewer: Yajuan Sun (Beijing)
Spectrally accurate space-time solution of Manakov systems. (English) Zbl 1439.65220
Reviewer: Marius Ghergu (Dublin)
Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems. (English) Zbl 1441.65062
Reviewer: Yajuan Sun (Beijing)
Conjugate-symplecticity properties of Euler-Maclaurin methods and their implementation on the infinity computer. (English) Zbl 1440.65273
Reviewer: Bülent Karasözen (Ankara)
The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions. (English) Zbl 1434.65111
Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation. (English) Zbl 1439.37079
Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations. (English) Zbl 1433.65207
Two kinds of new energy-preserving schemes for the coupled nonlinear Schrödinger equations. (English) Zbl 1486.65210
High-order energy-conserving line integral methods for charged particle dynamics. (English) Zbl 1452.65392
Locally conservative finite difference schemes for the modified KdV equation. (English) Zbl 1436.65100
Reviewer: Bülent Karasözen (Ankara)
A note on the continuous-stage Runge-Kutta(-Nyström) formulation of Hamiltonian boundary value methods (HBVMs). (English) Zbl 1433.65123
High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods. (English) Zbl 1429.65299
Symmetric integrators based on continuous-stage Runge-Kutta-Nyström methods for reversible systems. (English) Zbl 1429.65155
Conservative finite difference scheme for the nonlinear fourth-order wave equation. (English) Zbl 1429.65177
A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach. (English) Zbl 1428.65028
Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems. (English) Zbl 1448.65266
Global error bounds of one-stage extended RKN integrators for semilinear wave equations. (English) Zbl 1422.65229
Spectrally accurate energy-preserving methods for the numerical solution of the “good” Boussinesq equation. (English) Zbl 1418.65117
Arbitrary high-order EQUIP methods for stochastic canonical Hamiltonian systems. (English) Zbl 1426.60076
On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems. (English) Zbl 1434.65311
Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation. (English) Zbl 1414.65024
Reviewer: Anouar Ben Mabrouk (Sousse)
A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator. (English) Zbl 1470.65205
On a class of conjugate symplectic Hermite-Obreshkov one-step methods with continuous spline extension. (English) Zbl 1432.65017
Axioms 7, No. 3, Paper No. 58, 18 p. (2018); correction ibid. 8, No. 2, Paper No. 59, 6 p. (2019).
New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions. (English) Zbl 1429.65189
Partitioned averaged vector field methods. (English) Zbl 1398.65331
MSC:
65P10
A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic. (English) Zbl 1540.65188
MSC:
65L05
Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations. (English) Zbl 1368.65114
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