DOI10.1007/s10440-009-9513-6zbMath1192.65111OpenAlexW2015942421MaRDI QIDQ970519
Theodore E. Simos
Publication date: 19 May 2010
Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10440-009-9513-6
New three-stages symmetric six-step finite difference method with vanished phase-lag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions ⋮
New hybrid two-step method with optimized phase and stability characteristics ⋮
New Runge-Kutta type symmetric two-step method with optimized characteristics ⋮
A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation ⋮
An economical eighth-order method for the approximation of the solution of the Schrödinger equation ⋮
An implicit symmetric linear six-step methods with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation and related problems ⋮
A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation ⋮
Family of symmetric linear six-step methods with vanished phase-lag and its derivatives and their application to the radial Schrödinger equation and related problems ⋮
A family of embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation: development and theoretical analysis ⋮
A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation ⋮
Functionally-fitted block methods for second order ordinary differential equations ⋮
On ninth order, explicit Numerov-type methods with constant coefficients ⋮
New five-stages two-step method with improved characteristics ⋮
A new high algebraic order four stages symmetric two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems ⋮
A family of two stages tenth algebraic order symmetric six-step methods with vanished phase-lag and its first derivatives for the numerical solution of the radial Schrödinger equation and related problems ⋮
A new eight algebraic order embedded explicit six-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation ⋮
A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems ⋮
Stability and convergence of an effective finite element method for multiterm fractional partial differential equations ⋮
Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation ⋮
New phase fitted and amplification fitted Numerov-type methods for periodic IVPs with two frequencies ⋮
A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation ⋮
A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation ⋮
High order four-step hybrid method with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation ⋮
New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. I: construction and theoretical analysis ⋮
A new optimized Runge-Kutta pair for the numerical solution of the radial Schrödinger equation ⋮
An efficient and economical high order method for the numerical approximation of the Schrödinger equation ⋮
A generator of families of two-step numerical methods with free parameters and minimal phase-lag ⋮
A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮
A multistep method with optimal properties for second order differential equations ⋮
A four stages numerical pair with optimal phase and stability properties ⋮
A finite difference pair with improved phase and stability properties ⋮
A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems ⋮
New two stages high order symmetric six-step method with vanished phase-lag and its first, second and third derivatives for the numerical solution of the Schrödinger equation ⋮
New stable closed Newton-Cotes trigonometrically fitted formulae for long-time integration ⋮
A note on nonlocal boundary value problems for hyperbolic Schrödinger equations ⋮
Symplectic partitioned Runge-Kutta methods with the phase-lag property ⋮
A hybrid finite difference pair with maximum phase and stability properties ⋮
New finite difference pair with optimized phase and stability properties ⋮
Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag ⋮
A matrix method for determining eigenvalues and stability of singular neutral delay-differential systems ⋮
Phase fitted symplectic partitioned Runge-Kutta methods for the numerical integration of the Schrödinger equation ⋮
A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems ⋮
Error upper bounds for a computational method for nonlinear boundary and initial-value problems ⋮
An optimized Runge-Kutta method for the numerical solution of the radial Schrödinger equation ⋮
A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation ⋮
New four-stages symmetric six-step method with improved phase properties for second order problems with periodical and/or oscillating solutions ⋮
New Runge-Kutta type symmetric two step finite difference pair with improved properties for second order initial and/or boundary value problems ⋮
A new multistep method with optimized characteristics for initial and/or boundary value problems ⋮
New multiple stages scheme with improved properties for second order problems ⋮
Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation ⋮
An explicit four-step method with vanished phase-lag and its first and second derivatives ⋮
Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 2: Kernel separability, space extension, and, series solution via telescopic matrices ⋮
A Runge-Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equation ⋮
A new explicit hybrid four-step method with vanished phase-lag and its derivatives ⋮
Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation ⋮
An explicit linear six-step method with vanished phase-lag and its first derivative ⋮
A family of explicit linear six-step methods with vanished phase-lag and its first derivative ⋮
A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation ⋮
The applications of algebraic methods on stable analysis for general differential dynamical systems with multidelays ⋮
A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation ⋮
New three-stages symmetric two step method with improved properties for second order initial/boundary value problems ⋮
New 8-step symmetric embedded predictor-corrector (EPCM) method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation ⋮
New hybrid symmetric two step scheme with optimized characteristics for second order problems ⋮
A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equation ⋮
A high algebraic order predictor-corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problems ⋮
Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equation ⋮
A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation ⋮
A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation ⋮
Exponentially fitted TDRK pairs for the Schrödinger equation ⋮
A new multistep finite difference pair for the Schrödinger equation and related problems ⋮
A new two-step finite difference pair with optimal properties ⋮
An efficient numerical method for the solution of the Schrödinger equation ⋮
A new two stages tenth algebraic order symmetric six-step method with vanished phase-lag and its first and second derivatives for the solution of the radial Schrödinger equation and related problems ⋮
Two stages six-step method with eliminated phase-lag and its first, second, third and fourth derivatives for the approximation of the Schrödinger equation ⋮
High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation ⋮
High algebraic order Runge-Kutta type two-step method with vanished phase-lag and its first, second, third, fourth, fifth and sixth derivatives ⋮
Trigonometrically fitted two-step Obrechkoff linear methods for the Schrödinger equation ⋮
A three-stages multistep teeming in phase algorithm for computational problems in chemistry ⋮
A four-stages multistep fraught in phase method for quantum chemistry problems ⋮
Explicit, eighth-order, four-step methods for solving \(y^{\prime\prime}=f(x, y)\) ⋮
A smooth approximation based on exponential spline solutions for nonlinear fourth order two point boundary value problems ⋮
Explicit Runge-Kutta methods for starting integration of Lane-Emden problem ⋮
A new explicit four-step method with vanished phase-lag and its first and second derivatives ⋮
A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation ⋮
New \(4(3)\) pairs diagonally implicit Runge-Kutta-Nyström method for periodic IVPs ⋮
High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation ⋮
Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives ⋮
Neural network solution of single-delay differential equations ⋮
Eighth order, phase-fitted, six-step methods for solving \(y^{\prime \prime}=f(x,y)\) ⋮
Algorithm for the development of families of numerical methods based on phase-lag Taylor series ⋮
A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation ⋮
A multistage two-step fraught in phase scheme for problems in mathematical chemistry ⋮
A Runge-Kutta type crowded in phase algorithm for quantum chemistry problems ⋮
A two-step modified explicit hybrid method with step-size-dependent parameters for oscillatory problems ⋮
A perfect in phase FD algorithm for problems in quantum chemistry ⋮
A multiple stage absolute in phase scheme for chemistry problems ⋮
Exponential and trigonometrical fittings: user-friendly expressions for the coefficients ⋮
Bounds for variable degree rational \(L_\infty\) approximations to the matrix exponential ⋮
A Runge-Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation ⋮
A predictor-corrector explicit four-step method with vanished phase-lag and its first, second and third derivatives for the numerical integration of the Schrödinger equation
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