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Ninth-order,explicit, two-step methods for second-order inhomogeneous linear IVPs |
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| Authors: | Vladislav N Kovalnogov Theodore E Simos Charalampos Tsitouras |
| Affiliation: | 1. Ulyanovsk State Technical University, 32 Severny Venets St., 432027 Ulyanovsk, Russia
Group of Numerical and Applied Mathematics on Urgent Problems of Heat and Mass Transfer, South Ural State University, 76 Lenin Ave., 454080 Chelyabinsk, Russia;2. South Ural State University, 76 Lenin Ave., 454080 Chelyabinsk, Russia;3. General Department, National and Kapodistrian University of Athens, Euripus Campus GR34400, Greece |
| Abstract: | 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. |
| Keywords: | hybrid Numerov methods initial value problem numerical solution |
