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International Journal of Computer Mathematics Volume 46, 1992 - Issue 1-2
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Original Articles

Two-step almost p-stable complete in phase methods for the numerical integration of second order periodic initial-value problems

T. E. Simos Department of Mathematics, National Technical University of Athens, Zografou Campus, Zografou, Athens, 157 73, Greece
Pages 77-85 | Received 18 Dec 1990, Published online: 19 Mar 2007

Citations (23)

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Read on this site (1)

T.E. Simos. (1998) An Accurate Exponentially-Fitted Four-Step Method for the Numerical Solution of the Radial Schrödinger Equation. Molecular Simulation 20:5, pages 285-301.
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Articles from other publishers (22)

Oluwasegun M. Ibrahim & Monday N. O. Ikhile. (2020) A Generalized Family of Symmetric Multistep Methods with Minimal Phase-Lag for Initial Value Problems in Ordinary Differential Equations. Mediterranean Journal of Mathematics 17:3.
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A. Konguetsof. (2011) A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation. Journal of Mathematical Chemistry 49:7, pages 1330-1356.
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Ibraheem Alolyan & T. E. Simos. (2010) A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation. Journal of Mathematical Chemistry 49:3, pages 711-764.
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Ibraheem Alolyan & T. E. Simos. (2010) Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation. Journal of Mathematical Chemistry 48:4, pages 1092-1143.
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Ibraheem Alolyan & T. E. Simos. (2010) High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation. Journal of Mathematical Chemistry 48:4, pages 925-958.
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A. Konguetsof. (2010) Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation. Journal of Mathematical Chemistry 48:2, pages 224-252.
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A. Konguetsof. (2009) A new two-step hybrid method for the numerical solution of the Schrödinger equation. Journal of Mathematical Chemistry 47:2, pages 871-890.
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D. S. Vlachos, Z. A. Anastassi & T. E. Simos. (2009) High order phase fitted multistep integrators for the Schrödinger equation with improved frequency tolerance. Journal of Mathematical Chemistry 46:4, pages 1009-1049.
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Z. A. Anastassi, D. S. Vlachos & T. E. Simos. (2009) A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems. Journal of Mathematical Chemistry 46:4, pages 1158-1171.
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T. E. Simos. (2009) A new Numerov-type method for the numerical solution of the Schrödinger equation. Journal of Mathematical Chemistry 46:3, pages 981-1007.
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D. S. Vlachos, Z. A. Anastassi & T. E. Simos. (2009) High order multistep methods with improved phase-lag characteristics for the integration of the Schrödinger equation. Journal of Mathematical Chemistry 46:2, pages 692-725.
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Z. A. Anastassi, D. S. Vlachos & T. E. Simos. (2009) A new methodology for the development of numerical methods for the numerical solution of the Schrödinger equation. Journal of Mathematical Chemistry 46:2, pages 621-651.
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G. A. Panopoulos, Z. A. Anastassi & T. E. Simos. (2009) Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. Journal of Mathematical Chemistry 46:2, pages 604-620.
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Liviu Gr. Ixaru & Guido Vanden BergheLiviu Gr. Ixaru & Guido Vanden Berghe. 2004. Exponential Fitting. Exponential Fitting 145 222 .
Ishtiaq Rasool Khan & Ryoji Ohba. (2000) New finite difference formulas for numerical differentiation. Journal of Computational and Applied Mathematics 126:1-2, pages 269-276.
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T.E. Simos & P.S. Williams. (1999) On finite difference methods for the solution of the Schrödinger equation. Computers & Chemistry 23:6, pages 513-554.
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T.E. Simos. (1999) Explicit exponentially fitted methods for the numerical solution of the Schrödinger equation. Applied Mathematics and Computation 98:2-3, pages 185-198.
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T. E. SIMOS. (2012) AN ACCURATE EXPONENTIALLY FITTED EXPLICIT FOUR-STEP METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION. International Journal of Modern Physics A 13:15, pages 2613-2626.
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T. E. Simos. (2011) An Accurate Method for the Numerical Solution of the Schrödinger Equation. Modern Physics Letters A 12:26, pages 1891-1900.
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T. E. Simos. (1997) An Exponentially Fitted Method for the Numerical Solution of the Schrödinger Equation. Journal of Chemical Information and Computer Sciences 37:2, pages 343-348.
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P. S. Williams & T. E. Simos. 1997. Numerical Analysis and Its Applications. Numerical Analysis and Its Applications 565 572 .
T. E. Simos. (2004) Predictor–corrector phase‐fitted methods for Y ″ = F ( X , Y ) and an application to the Schrödinger equation . International Journal of Quantum Chemistry 53:5, pages 473-483.
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