Keywords: 65L04; 65L05; 65L10; 65L20; 65L50; 65Y15; Initial value problem; Boundary value problem; Stiffness; Simple shooting method; Multiple shooting method; The Troesch's problem;
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Keywords: Chaotic system; Fractional differential equation; Local and global stability; Numerical simulations; Relative error; Spatiotemporal oscillations; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Keywords: Positivity; Exponential integrators; Nonlinear differential equations; Numerical methods; 65L05; 65P40; 65L20;
Keywords: Atangana-Baleanu-Caputo derivative; Fractional reaction-diffusion; Hopf bifurcation; Spatiotemporal system; Oscillations; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10,;
Keywords: Exponential time-integrator; Fractional reaction-diffusion; Nonlinear PDEs; Numerical simulations; Hopf-bifurcation; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Keywords: 65L05; 65L06; Exponential fitting; Modified two-step hybrid methods; Oscillatory second-order IVPs;
Keywords: Nonlinear Hamiltonian wave equation; Finite difference discretization; Neumann boundary conditions; Energy-preserving algorithm; AVF formula; Oscillatory system; 35C15; 35L05; 35L70; 65L05; 65L06;
Keywords: 65L05; 65L20; 65L70; Stiff ordinary differential equation; Implicit two-step peer method; A-stability; Double quasi-consistency; Embedded method global error estimation;
Keywords: 65L05; 65F30; 49J20; Dynamical low-rank approximation; Differential Lyapunov equations; Differential Riccati equations; Linear quadratic regulator problem; Splitting integrators; El Niño simulation;
Keywords: 41A05; 65D05; 65L05; 65D32; Bivariate function approximation; Lagrange polynomial expansion; Bernoulli polynomial expansion; Poisson boundary value problems; Numerical cubature;
Keywords: 26A33; 65L70; 65L05; Fractional differential equation; Caputo fractional derivative; Riemann-Liouville fractional derivative; Error estimates; Hadamard finite-part integral;
Keywords: 65L05; 65L06; Initial value problem; Numerical solution; Variable step; Phase fitted; Runge-Kutta;
Keywords: Fractional differential equation; Caputo fractional derivative; Volterra integral equation; Adapted mesh; Convergence analysis; 65L05; 65R20; 65L20;
Keywords: 65L05; Implicit peer methods; Stiff ODE systems; Zero stability; Superconvergence;
Keywords: Caputo derivative; Exponential integrator; Fractional reaction-diffusion; Hopf bifurcation; Oscillations; Predator-prey system; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Keywords: Circuit-breaking algorithm; Monotone system; Input/output characteristic; MAPK signaling pathway; 34A09; 34A34; 65L05; 65L15; 65S05; 92B05; 93D25;
Keywords: 34A34; 35A05; 35K57; 65L05; 65M06; 93C10; Fourier spectral method; Exponential integrator; Fractional reaction-diffusion; Nonlinear PDEs; Numerical simulations; Spatiotemporal structures;
Keywords: 65L05; 65L06; 65L20; 65L50; 65L70; Ordinary differential equation; Stiff problem; Singly diagonally implicit two-step peer method; Absolute and scaled local and global error estimations; Automatic local and global error controls;
Keywords: Attractor; Lorenz system; Chen system; Nose-Hoover oscillator; Power series; Region of convergence; Almost periodic function; 34D45; 37D45; 65G20; 65G50; 65L05; 65L07; 65L20; 65P20; 65L70;
Keywords: Asymptotically stable; Exponential time differencing methods; Fractional reaction-diffusion; Pattern formation; Nonlinear time-dependent PDEs; Stability analysis; Super-diffusion; 92D25; 65L05; 65M06; 65N20; 70K50; 35B35;
Keywords: 65L05; 65L06SSP; Positivity; Explicit peer methods; Nonstiff initial value problems
Keywords: Fractional exponential integrators; Fourier transform; Fractional reaction–diffusion system; Pattern formation; Turing instability35A05; 35K57; 65L05; 65M06; 93C10
Keywords: Fractional-order Legendre functions; Time-fractional convection–diffusion equation; Operational matrix34A08; 45P05; 65L05
Keywords: 65L05; 34A08; 26A33Fractional calculus; Caputo derivative; Boundary value problem; Nonpolynomial collocation method
Keywords: 65L05; 65L12; 65L20; 65L70Singularly perturbed; Initial value problem; Adaptive grid; Uniform convergence
Keywords: Monotone iterative technique; Deviating arguments; Riemann–Liouville fractional derivative; Numerical iterative scheme34A08; 34A45; 65L05
Keywords: 65L05; 65L06; 65L20; 65M20Initial value problem; Method of lines (MOL); Multistep methods; Monotonicity; Boundedness; Strong-stability-preserving (SSP)
Keywords: 65L03; 65L05; 65L06; 65L20; 65R20Delay-differential equations; Threshold conditions; Continuous Runge–Kutta methods; Bisection method; Local error estimation; Convergence analysis
Keywords: 65L05; 65L20General linear methods; Order conditions; Nordsieck methods; Two-step Runge–Kutta formulas
Keywords: 65L05; 65L06; 65L20; 65L50; 65L70Ordinary differential equations; Superconvergent explicit peer methods; Absolute and scaled local and global error estimations; Local and global error control
Keywords: 65L05; 65L07; 65L20; Neutral systems; Unstable difference operators; Stability criterion;
Keywords: 65L05; 65L11; 65L80Singularly perturbed ODEs; Quasistatic approximation; Multibody system model
Keywords: 65L05; 65L80; 65L20; Dynamic iteration; Cosimulation; PDAE; Coupling;
Keywords: 65L05; 65Y05; 65P10Hamiltonian differential equations; Parareal algorithm; Parallel architectures; Symplectic methods; Backward error analysis; Long-time integration
Keywords: 65L05; 65L20; General linear methods; Order and stage order; Order conditions; A- and L-stability; Construction of highly stable methods; Error propagation;
Keywords: 65L05; 65L06; 34C15; 34E05Trigonometric collocation methods; Lagrange polynomials; Multi-frequency oscillatory second-order systems; Variation-of-constants formula
The projected explicit Itô-Taylor methods for stochastic differential equations under locally Lipschitz conditions and polynomial growth conditions
Keywords: 60H10; 65L05; 65L20; The projected explicit Itô-Taylor methods; Stochastic differential equations; Stochastic C-stability; Stochastic B-consistency;
Analysis and numerical simulation of multicomponent system with Atangana-Baleanu fractional derivative
Keywords: Mittag-Leffler; Fractional derivative; Hopf-bifurcation; Oscillations; Predator-prey; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations
Keywords: Caputo derivative; Difference methods; Fractional subdiffusion-reaction systems; Pattern formation; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems
Keywords: 65F10; 65L05; 65N22; Linear systems; Stationary iterative methods; SOR method; Dynamical systems; Gradient systems; Discrete gradient methods;
An efficient numerical method for a two-point boundary value problem with a Caputo fractional derivative
Keywords: 65L05; 65L12; 65L20; Caputo fractional derivative; Boundary value problem; Shooting method; integral-differential equation; Convergence analysis;
Weak delay-dependent stability of Runge-Kutta methods for differential systems with distributed delays
Keywords: 65L05; 65L07; 65L20; Differential systems with distributed delays; Weak delay-dependent stability; Pouzet-type Runge-Kutta methods; Argument principle;
Symplectic integrators for second-order linear non-autonomous equations
Keywords: 65L07; 65L05; 65Z05; Second-order linear differential equations; Non-autonomous; Symplectic integrators; Magnus expansion; Matrix Hill's equation;
Energy-conserving methods for the nonlinear Schrödinger equation
Keywords: Hamiltonian partial differential equations; Nonlinear Schrödinger equation; Energy-conserving methods; Line integral methods; Hamiltonian Boundary Value methods; HBVMs; 65P10; 65M20; 65L05;
Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources
Keywords: 65F60; 65F30; 65N22; 65L05; 35Q61; Light scattering; Mesoscopic optics; Disordered media; Finite difference time domain (FDTD) methods; Krylov subspace methods; Exponential time integration;
Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
Keywords: 65P10; 65L05; Gauss collocation methods; Symplectic methods; Energy-conserving methods; Line integral methods; Hamiltonian problems; Poisson problems;
A first approach in solving initial-value problems in ODEs by elliptic fitting methods
Keywords: 65L05; 65L20; Initial value problems; Elliptic fitting method; Perturbed Duffing oscillator;
An integro quadratic spline approach for a class of variable-order fractional initial value problems
Keywords: Variable-order fractional calculus; Spline approximation; Integro spline; Bagley-Torvik fractional equation; Basset fractional equation; 26A33; 34A08; 33F05; 41A15; 65L12; 65L05;
Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative
Keywords: Caputo-Fabrizio derivative; Fractional Adams-Bashforth method; Error analysis; Nonlinear chaotic systems; Numerical simulations; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense
Keywords: Caputo-Fabrizio derivative; Exponential decay-law; Exponential time differencing; Finite difference method; Fractional nonlinear PDEs; Numerical simulations; Riemann-Liouville definition; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;