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Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2018, Volume 41, Issue 5, pp. 1845 - 1854
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2019, Volume 42, Issue 18, pp. 7349 - 7358
The classical four‐stage family of explicit sixth‐order Numerov‐type method is considered. We provide two kinds of interpolants: (a) a three‐step interpolation... 
y″=f(x,y) | explicit hybrid Numerov | interpolation | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | HYBRID 4-STEP METHODS | y ''=f(x | SCHRODINGER-EQUATION | 2-STEP METHODS | HIGH-ORDER | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | EFFICIENT INTEGRATION | y | RUNGE-KUTTA PAIRS | P-STABLE METHOD | Interpolation | Mathematical analysis
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2020, Volume 43, Issue 3, pp. 1204 - 1215
The explicit sixth‐order Numerov‐type family of methods is considered. A new representative from this family is produced and equipped with a cheap step‐size... 
variable step | y″ = f (x, y) | explicit hybrid Numerov | MATHEMATICS, APPLIED | SOLVING Y | HIGH-ORDER | VANISHED PHASE-LAG | y '' = f (x | 6TH ORDER | SYMBOLIC DERIVATION | RUNGE-KUTTA PAIRS | P-STABLE METHOD | 4-STEP METHODS | 2-STEP HYBRID METHODS | NOUMEROV-TYPE METHOD | Algorithms
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2019, Volume 42, Issue 18, pp. 7047 - 7058
The classical explicit fourth‐order Numerov‐type method is considered. The equations of condition for deriving the corresponding interpolants are given. Then... 
variable step | explicit hybrid Numerov | y″=(x,y) | MATHEMATICS, APPLIED | HYBRID 4-STEP METHODS | SOLVING Y | y '' = (x, y) | 2-STEP METHODS | NUMERICAL-SOLUTION | FITTED MODIFICATIONS | 6TH ORDER | SYMBOLIC DERIVATION | RUNGE-KUTTA PAIRS | PHASE-LAG-ORDER | F X
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 8/2018, Volume 15, Issue 4, pp. 1 - 16
An effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for the solution of the special second-order initial value problem.... 
second order | Initial value problem | Primary 65L05 | Mathematics, general | Secondary 65L06 | phase-lag | Mathematics | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | INITIAL-VALUE-PROBLEMS | SCHRODINGER-EQUATION | HIGH-ORDER | 2ND-ORDER LINEAR IVPS | MATHEMATICS | NUMERICAL-INTEGRATION | RUNGE-KUTTA PAIRS | P-STABLE METHOD | 2-STEP HYBRID METHODS | NOUMEROV-TYPE METHOD
Journal Article
Journal of Mathematical Chemistry, ISSN 0259-9791, 5/2018, Volume 56, Issue 5, pp. 1456 - 1466
Journal Article
Numerical Algorithms, ISSN 1017-1398, 9/2003, Volume 34, Issue 1, pp. 27 - 40
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2003, Volume 45, Issue 1, pp. 37 - 42
We present in this paper a new approach for the derivation of hybrid explicit Numerov type methods. The new methodology does not require the intermediate use... 
Hybrid methods | Two step methods | Numerical solution | Initial value problem | numerical solution | MINIMAL PHASE-LAG | MATHEMATICS, APPLIED | initial value problem | two step methods | SCHRODINGER-EQUATION | NUMERICAL-INTEGRATION | hybrid methods | NOUMEROV-TYPE METHOD | INITIAL-VALUE PROBLEMS
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2019, Volume 42, Issue 18, pp. 6301 - 6314
A semi‐implicit family of two‐step methods is considered for the numerical solution of y′′=f(x,y). These methods are hybrid and waste two stages (function... 
y′′=f(x,y) | periodic problems | Numerov | ode15s | MATHEMATICS, APPLIED | HYBRID 4-STEP METHODS | NUMEROV-TYPE METHODS | SOLVING Y | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | FITTED MODIFICATIONS | MULTISTEP METHODS | y '' = f(x, y) | 6TH ORDER | SYMBOLIC DERIVATION | RUNGE-KUTTA PAIRS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2007, Volume 186, Issue 2, pp. 1385 - 1394
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2017, Volume 40, Issue 14, pp. 5286 - 5294
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 01/2016, Volume 273, pp. 493 - 505
The construction of exponentially fitted (EF) two-step hybrid methods for the numerical integration of oscillatory second-order IVPs is analyzed. These methods... 
Exponential fitting | Oscillatory second-order IVPs | Two-step hybrid methods | MATHEMATICS, APPLIED | NUMEROV | ODES | RUNGE-KUTTA METHOD | INITIAL-VALUE PROBLEMS
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2019, Volume 42, Issue 6, pp. 2025 - 2032
A four‐step method of seventh algebraic order is presented. It is tuned for addressing the special second order initial value problem. The new method is... 
variable coefficients | hybrid methods | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | NUMEROV-TYPE METHODS | SCHRODINGER-EQUATION | NUMERICAL-SOLUTION | LAG-ORDER | MULTISTEP METHODS | EFFICIENT INTEGRATION | SYMBOLIC DERIVATION | RUNGE-KUTTA PAIRS | P-STABLE METHOD | Boundary value problems
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2019, Volume 42, Issue 2, pp. 710 - 716
A two–stage, explicit, hybrid four–step method of sixth order for the solution of the special second order initial value problem is presented here. The new... 
variable coefficients | hybrid methods | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED |