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Phase‐fitted, six‐step methods for solving x ′ ′ = f ( t , x )
Author(s) -
Liu Chenglian,
Hsu ChiehWen,
Simos T. E.,
Tsitouras Ch.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5623
Subject(s) - mathematics , simple (philosophy) , function (biology) , set (abstract data type) , variance (accounting) , order (exchange) , phase (matter) , derivative (finance) , mathematical analysis , quantum mechanics , philosophy , accounting , epistemology , finance , evolutionary biology , computer science , economics , financial economics , business , biology , programming language , physics
An explicit, six‐step method of sixth order is presented and tuned for the numerical solution of x ′ ′ = f ( t , x ). This method is explicit, hybrid, and uses two function evaluations (stages) per step. Its coefficients are varied and depend on the step size. This variance comes from the demand of the method to nullify the phase errors produced when solving the standard simple oscillator. The first and second derivative of this error vanish also. Numerical tests in a set of relevant problems illustrate the efficiency of the newly derived method.