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Ninth‐order, explicit, two‐step methods for second‐order inhomogeneous linear IVPs
Author(s) -
Kovalnogov Vladislav N.,
Simos Theodore E.,
Tsitouras Charalampos
Publication year - 2020
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.6246
Subject(s) - mathematics , initial value problem , order (exchange) , set (abstract data type) , constant (computer programming) , ninth , value (mathematics) , calculus (dental) , mathematical analysis , computer science , statistics , economics , programming language , medicine , physics , dentistry , finance , acoustics
In the present paper, the second‐order linear inhomogeneous initial value problems (LI‐IVP) with constant coefficients is of our interest. Two‐step hybrid methods (ie, of Numerov‐type) are considered for addressing this problem. Thus, a special set of order conditions is given and solved for derivation a low cost new method. Actually, we manage to save two stages per step. This is crucial as shown in various numerical tests where our new proposal outperforms standard methods in the relevant literature.