New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration

By T. E. Simos. 2003

151 citations recorded by the source corpus.

The closed Newton-Cotes differential methods of high algebraic order for small number of function evaluations are unstable. In this work, we propose a new closed Newton-Cotes trigonometrically fitted differential method of high algebraic order which gives much more efficient results than the well-know ones.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2fbb56e1da371290736f1d2b4cd05471e90253dc

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In Computational Theory and Mathematics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

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 (2015, methodology): “The last decades many methodologies have been proposed in the literature for the estimation of the local truncation error (LTE) on the numerical solution of systems of differential equations (see for example [1–57]).”
A new family of 7 stages, eighth‐order explicit Numerov‐type methods (2017, methodology): “Simos11 added many stages for achieving an eighth-order method while Tsitouras and Simos12 gave an eighth algebraic order explicit method with 10 stages and phase-lag order 14, reducing drastically the required number of stages per step.”
Trigonometric fitted, eighth‐order explicit Numerov‐type methods (2018, methodology): “Then, Simos11 used a lot additional stages for an eighth-order method while Tsitouras and Simos12 used 10 stages for an eighth-order method with 14th phase-lag order.”
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 (2015, background): “Much research has been done the last decades on the estimation of the LTE for the numerical solution of systems of differential equations (see for example [1–56]).”
A family of explicit linear six-step methods with vanished phase-lag and its first derivative (2014, methodology): “(see for more details [1–121] and references therein).”
Evolutionary generation of high‐order, explicit, two‐step methods for second‐order linear IVPs (2017, methodology): “In parallel, our group has dealt in-depth with various types of multistep methods, Runge-Kutta & RKN methods, and especially fitted methods for addressing Equation 2, see previous studies.(16-43) Here, we will extend the results of Tsitouras(14) introducing an eighth algebraic order method at a cost”
High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation (2012, methodology): “– The classical fourth order closed Newton-Cotes formulae (Method I) – The classical sixth order closed Newton-Cotes formulae (Method II) – The classical eighth order closed Newton-Cotes formulae (Method III) – The closed Newton-Cotes formulae developed in [69] (Method IV) – The closed Newton-Cotes ”