Keywords: 65M20; 65L06; 65R10; 26A33; Multi-term time-fractional diffusion equation; Numerical method; Stability; Convergence; Method of separation of variables; Energy method;
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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: Finite volume schemes; Stiff problems; Runge-Kutta methods; Implicit-explicit schemes; Hyperbolic systems; Relaxation; 65M08; 65L04; 65L06; 35L45;
Keywords: 65L05; 65L06; Initial value problem; Numerical solution; Variable step; Phase fitted; Runge-Kutta;
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: Fractional differential equations; Caputo derivatives; Adams methods; Initial value problems; Fractional partial differential equations; 26A33; 65L06; 65L20;
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: 65L06; 65G50; 65P10Symmetric linear multistep methods; Constrained Hamiltonian systems; Propagation of round-off error
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: 65L06; 34A08; 34A36; 47N70Fractional differential equation; Discontinuous problem; Set-valued regularization; Implicit method; Fractional Adams method
Keywords: Improved Falkner-type methods; Oscillatory second-order differential equations; Global error bounds65L05; 65L06; 65L20
Keywords: 65L05; 65L06; 34C15; 34E05Trigonometric collocation methods; Lagrange polynomials; Multi-frequency oscillatory second-order systems; Variation-of-constants formula
Block Nyström type integrator for Bratu's equation
Keywords: 65L06; 65L20; Block Nyström method; One dimensions Bratu's equations; Convergence; Rate of convergence;
Asymptotic mean-square stability of weak second-order balanced stochastic Runge-Kutta methods for multi-dimensional Itô stochastic differential systems
Keywords: Stochastic differential equations; Multi-dimensional systems; Numerical solutions; Stochastic Runge--Kutta methods; Mean-square stability analysis; Balanced stochastic Runge-Kutta methods; 60H10; 60H35; 65L06; 65L20;
Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving yâ²â²â²=f(x,y)
Keywords: Enumeration of trees; Symbolic generation of trees; Order conditions; Differential evolution; 65L05; 65L06; 68W30; 90C59;
On A-stable one-leg methods for solving nonlinear Volterra functional differential equations
Keywords: Nonlinear Volterra functional differential equations; Contractivity; Asymptotic stability; Bounded stability; One-leg methods; A-stability; 65L03; 65L06; 65L07; 65L20;
An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method
Keywords: Partial differential equations; Differential quadrature method; Strong stability-preserving Runge-Kutta; Modified Cubic B-splines; Schrödinger equation; 65M99; 65D07; 65L06;
Stability of the Richardson Extrapolation combined with some implicit Runge-Kutta methods
Keywords: 65L05; 65L06; 65L04; Systems of ODEs; Implicit Runge-Kutta methods; Richardson Extrapolation; Stability properties; Atmospheric chemical scheme;
Efficient goal-oriented global error estimators for BDF methods using discrete adjoints
Keywords: 65L05; 65L06; 65L60; 65L20; 65L70; BDF methods; Discrete adjoints; Petrov-Galerkin discretization; Global error estimation; Dual weighted residual methodology;
On modifications of Runge–Kutta–Nyström methods for solving y(4)=f(x,y)y(4)=f(x,y)
Keywords: Enumeration of trees; Symbolic generation of trees; Order conditions; Differential Evolution65L05; 65L06; 68W30; 90C59
Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs
Keywords: Exponential fitting; Two-step hybrid methods; Oscillatory second-order IVPs65L05; 65L06
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Keywords: 65L06; 65M06; 65M20Implicit–explicit (IMEX) multistep methods; Monotonicity; Boundedness; TVD; TVB; Stability
Application of approximate matrix factorization to high order linearly implicit Runge–Kutta methods
Keywords: 65L04; 65L06; 65M20Approximate matrix factorization; Linearly implicit Runge–Kutta methods; High order; Reaction–diffusion equations
On the benefits of the LDLTLDLT factorization for large-scale differential matrix equation solvers
Keywords: 15A23; 65L06; 93A15Large-scale; Matrix differential equations; Low-rank; Riccati equations; Lyapunov equations
A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems
Keywords: 65L05; 65L06; Large stiff systems; AMF; Peer methods; Krylov techniques;
Strong-stability-preserving, Hermite-Birkhoff time-discretization based on k step methods and 8-stage explicit Runge-Kutta methods of order 5 and 4
Keywords: primary; 65L06; secondary; 65M20; Strong stability preserving; Hermite-Birkhoff method; SSP coefficient; Time discretization; Method of lines; Comparison with other SSP methods;
Generalized Picard iterations: A class of iterated Runge-Kutta methods for stiff problems
Keywords: 65L04; 65L05; 65L06; Iterated Runge-Kutta methods; Radau methods; Stiff problems;
Special extended Nyström tree theory for ERKN methods
Keywords: primary; 65L05; 65L06; 65M20; 65N40; 65R20; Special extended Nyström trees; Second-order oscillatory problems; Extended Runge-Kutta-Nyström methods; Order conditions;
Solvability of concatenated Runge–Kutta equations for second-order nonlinear PDEs
Keywords: 65L06; 65H10Solvability; Concatenated Runge–Kutta methods; Homotopy continuation method
Symmetric and symplectic exponentially fitted Runge-Kutta-Nyström methods for Hamiltonian problems
Keywords: 65L05; 65L06; 65M20; 65N40; Runge-Kutta-Nyström method; Symmetry; Symplecticity; Exponential fitting; Hamiltonian system;
Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations
Keywords: 60H10; 65L05; 65L06; Order conditions; Multiplicative noise; Weak approximation;
An improved approximate Newton method for implicit Runge–Kutta formulas
Keywords: 65L06; 65H10Implicit Runge–Kutta; Radau IIA method; Stiff ODE systems; Modified Newton methods
A numerical ODE solver that preserves the fixed points and their stability
Keywords: 65L05; 65L06; 65L70Fixed points; Exact finite difference methods; Predictor–corrector method; Nonstandard finite-difference methods; Initial-value problems
Global error estimation and control in linearly-implicit parallel two-step peer W-methods
Keywords: 65L05; 65L06; 65L20; 65L50; 65L70; Ordinary differential equations; Linearly-implicit parallel peer W-methods; Local and global error estimations; Automatic global error control;
B-spline collocation for solution of two-point boundary value problems
Keywords: 65L05; 65L06; 65L07; 65L12; 65L20; 65L70; 65L80Nonlinear boundary value problems; Sextic B-spline method; Collocation; Convergence; Green’s function
Runge-Kutta methods for jump-diffusion differential equations
Keywords: 60H35; 60H10; 65C30; 60J75; 65L06; Runge-Kutta methods; Jump-diffusion; Small noise; Mean-square convergence;
Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations
Keywords: 65L06; 65L20Neutral delay integro-differential equations; Dynamical systems; Halanay inequality; Dissipativity; Asymptotic stability
Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation
Keywords: 65L05; 65L06; 65L20; 65L50Doubly quasi-consistent numerical schemes; Superconvergent explicit two-step peer methods; Embedded formulas; Adaptivity; Local error estimation; Automatic global error control
On some explicit Adams multistep methods for fractional differential equations
Keywords: 65L06; 65L20; 26A33Fractional differential equation; Numerical solution; Multistep method; Adams–Moulton; Adams–Bashforth; Explicit algorithm; Stability
Order conditions for ARKN methods solving oscillatory systems
Keywords: 65L05; 65L06; Adapted Runge-Kutta-Nyström methods; Order conditions; Oscillatory systems; B-Series;
A robust trigonometrically fitted embedded pair for perturbed oscillators
Keywords: 65L05; 65L06; Trigonometrically fitted ARKN methods; Perturbed oscillators; Embedded pairs;
Stability and asymptotic stability of θθ-methods for nonlinear stiff Volterra functional differential equations in Banach spaces
Keywords: 65L06; 65L20Stability; Asymptotic stability; Volterra functional differential equations; θθ-methods; Banach space
Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations
Keywords: 65L05; 65L06; 65L20Singularly perturbed systems; Volterra delay-integro-differential equations; Linear multistep methods; Error analysis; Quadrature rule
A Fourier method and an extrapolation technique for Stokes’ first problem for a heated generalized second grade fluid with fractional derivative
Keywords: 65M20; 65L06; 65R10; 26A33Stokes’ first problem; Heat flow; Numerical approximation; Stability; Convergence; Fourier method; Extrapolation method
Explicit methods for fractional differential equations and their stability properties
Keywords: 65L06; 65L20; 26A33Differential equation; Fractional order; Multistep method; Explicit method; Region of stability; Interval of stability
Multirate Runge–Kutta schemes for advection equations
Keywords: 65L06; 34-04Time integration; Runge–Kutta method; Multirate scheme; Flux splitting
Construction of a multirate RODAS method for stiff ODEs
Keywords: 65L06; 65L50; 65M06; 65M20Multirate time stepping; Local time stepping; High-order Rosenbrock methods; Ordinary differential equations
Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm
Keywords: 65L Except 65L05; 65L06; 65L07; 65L12; 65L20; 65L70; 65L80Boundary value problems; Degenerate problems; Pole detection; Singularity; Formally orthogonal Hadamard polynomials; qd-Algorithm; Finite difference scheme; Fröbenius method