Keywords: شرایط سفارش; Numerical stability; Partial differential equations; Finite difference methods; Skew-symmetric differentiation matrices; Order conditions;
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Keywords: شرایط سفارش; Hybrid method; Three-step method; B-series; Order conditions; Third order ordinary differential equations; Numerical integrator;
Keywords: شرایط سفارش; Trigonometrically fitted methods; Three-derivative Runge-Kutta methods; Order conditions; Explicit methods; Oscillatory initial value problems;
Keywords: شرایط سفارش; Trigonometrical-fitting; Two-step hybrid methods; Oscillatory problems; Generalized B2-series; Order conditions; Symmetry;
Keywords: شرایط سفارش; General linear methods; Order conditions; Starting procedures; Generalized Runge-Kutta methods;
Keywords: شرایط سفارش; General linear methods; Order conditions; Linear stability analysis; Prothero-Robinson problem; Stiff differential systems; Order reduction phenomenon;
Keywords: شرایط سفارش; Volterra integral equations; General linear methods; Order conditions; AA-stability; V0V0-stability; V0(α)V0(α)-stability
Keywords: شرایط سفارش; 65L05; 65L20General linear methods; Order conditions; Nordsieck methods; Two-step Runge–Kutta formulas
Keywords: شرایط سفارش; 65L05; 65L20; General linear methods; Order and stage order; Order conditions; A- and L-stability; Construction of highly stable methods; Error propagation;
Trigonometrically fitted multi-step RKN methods for second-order oscillatory initial value problems
Keywords: شرایط سفارش; Multi-step Runge-Kutta-Nyström methods; Order conditions; Trigonometrical fitting; Explicit methods; Oscillatory special second-order initial value problems;
Order conditions for stochastic Runge-Kutta methods preserving quadratic invariants of Stratonovich SDEs
Keywords: شرایط سفارش; Stratonovich SDEs; Stochastic Runge-Kutta methods; Quadratic invariants; Stochastic B-series; Order conditions;
Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving yâ²â²â²=f(x,y)
Keywords: شرایط سفارش; Enumeration of trees; Symbolic generation of trees; Order conditions; Differential evolution; 65L05; 65L06; 68W30; 90C59;
Generalized ROW-type methods for solving semi-explicit DAEs of index-1
Keywords: شرایط سفارش; Rosenbrock methods; W methods; Differential-algebraic equations; Order conditions; Approximated Jacobian;
Multi-step Runge-Kutta-Nyström methods for special second-order initial value problems
Keywords: شرایط سفارش; Multi-step Runge-Kutta-Nyström methods; Order conditions; Special Nyström-series; Explicit methods; Special second-order initial value problems;
General Nyström methods in Nordsieck form: Error analysis
Keywords: شرایط سفارش; Second order ordinary differential equations; Multi-value numerical methods; General Nyström methods; Error analysis; Order conditions
On modifications of Runge–Kutta–Nyström methods for solving y(4)=f(x,y)y(4)=f(x,y)
Keywords: شرایط سفارش; Enumeration of trees; Symbolic generation of trees; Order conditions; Differential Evolution65L05; 65L06; 68W30; 90C59
A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems
Keywords: شرایط سفارش; Multi-frequency oscillators; Nyström-tree theory; ERKN methods; Order conditions; B-series;
Embedded explicit Runge–Kutta type methods for directly solving special third order differential equations y‴=f(x,y)y‴=f(x,y)
Keywords: شرایط سفارش; RKD methods; Third-order ordinary differential equations; Embedded methods; Order conditions
Construction of algebraically stable DIMSIMs
Keywords: شرایط سفارش; General linear methods; Order conditions; Algebraic stability
On the construction of second derivative diagonally implicit multistage integration methods for ODEs
Keywords: شرایط سفارش; General linear methods; Two-derivative methods; Ordinary differential equation; Order conditions; A- and L-stability; Runge-Kutta stability;
Special extended Nyström tree theory for ERKN methods
Keywords: شرایط سفارش; primary; 65L05; 65L06; 65M20; 65N40; 65R20; Special extended Nyström trees; Second-order oscillatory problems; Extended Runge-Kutta-Nyström methods; Order conditions;
Direct integrators of Runge–Kutta type for special third-order ordinary differential equations
Keywords: شرایط سفارش; Third-order ordinary differential equations; RKT methods; Tri-colored trees; B-series; Order conditions; Collocation methods
Explicit Nordsieck methods with extended stability regions
Keywords: شرایط سفارش; Explicit Nordsieck methods; General linear methods; Order conditions; Region of absolute stability;
Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations
Keywords: شرایط سفارش; 60H10; 65L05; 65L06; Order conditions; Multiplicative noise; Weak approximation;
Nordsieck methods with computationally verified algebraic stability
Keywords: شرایط سفارش; Nordsieck methods; General linear methods; Order conditions; Algebraic stability;
A new class of exponential propagation iterative methods of Runge–Kutta type (EPIRK)
Keywords: شرایط سفارش; Exponential integrators; Krylov projections; Exponential propagation iterative (EPI) methods; Stiff systems; Newton–Krylov implicit methods; Order conditions; B-series; Large scale computing
Two-step extended RKN methods for oscillatory systems
Keywords: شرایط سفارش; Two-step extended Runge–Kutta–Nyström-type methods; BBTBBT-series; BBWTBBWT-series; Order conditions; Oscillatory systems
Extended RKN-type methods with minimal dispersion error for perturbed oscillators
Keywords: شرایط سفارش; 65L05; 65L06ERKN methods; Extended tree theory; Order conditions; Minimal dispersion error; Perturbed oscillators
General linear methods for Volterra integral equations
Keywords: شرایط سفارش; General linear methods; Volterra integral equations; Order conditions; Linear stability analysis; Convolution test equation
ERKN integrators for systems of oscillatory second-order differential equations
Keywords: شرایط سفارش; ERKN integrators; B-series; Order conditions; Oscillatory systems; Hamiltonian systems; Nonlinear wave equations
On the order of general linear methods
Keywords: شرایط سفارش; General linear methods; Order conditions; Ordinary differential equations
Note on derivation of order conditions for ARKN methods for perturbed oscillators
Keywords: شرایط سفارش; 02.60.Jh; 02.70.BfAdapted Runge–Kutta–Nyström methods; Order conditions; Nyström trees; B-Series
Order conditions for ARKN methods solving oscillatory systems
Keywords: شرایط سفارش; 65L05; 65L06; Adapted Runge-Kutta-Nyström methods; Order conditions; Oscillatory systems; B-Series;
Extended RKN-type methods for numerical integration of perturbed oscillators
Keywords: شرایط سفارش; 02.60.Jh; 02.70.BfExtended tree theory; Order conditions; Runge–Kutta–Nyström-type methods; Perturbed oscillators
Enumeration results for Runge–Kutta methods for index 2 DAEs
Keywords: شرایط سفارش; 65L06; 05C30Runge–Kutta methods; Index 2 DAEs; Order conditions; Enumeration
Symbolic derivation of order conditions for hybrid Numerov-type methods solving y″=f(x,y)y″=f(x,y)
Keywords: شرایط سفارش; Numerov-type methods; Order conditions; Rooted trees; Integer partitions; Truncation error; MATHEMATICA®MATHEMATICA®
Two-step almost collocation methods for Volterra integral equations
Keywords: شرایط سفارش; Two-step collocation methods; Volterra integral equations; Order conditions; Convergence; Stability analysis; A-stability
Order conditions for integrators and mappings with applications
Keywords: شرایط سفارش; primary; 65L05; 65L06; Runge-Kutta-like method; B-series; Two-step Runge-Kutta methods; Three-step Runge-Kutta methods; Linear multistep methods; Second-derivative linear multistep methods; Order conditions; Order conditions based on mappings;
The recursions of order conditions for some Runge–Kutta-like methods
Keywords: شرایط سفارش; Runge–Kutta-like method; B-series; Order conditions; Recursion of the order conditions
Starting methods for two-step Runge–Kutta methods of stage-order 3 and order 6
Keywords: شرایط سفارش; 65L05; 65L06; 65L20Two-step Runge–Kutta methods; Order reduction; Starting methods; Order conditions; Implementation
ARK methods: some recent developments
Keywords: شرایط سفارش; Almost Runge-Kutta methods; Runge-Kutta stability; Order conditions;