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Functional continuous Runge–Kutta methods with reuse. / Eremin, Alexey S.
в: Applied Numerical Mathematics, Том 146, 01.12.2019, стр. 165-181.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Functional continuous Runge–Kutta methods with reuse
AU - Eremin, Alexey S.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - In the paper explicit functional continuous Runge–Kutta and Runge–Kutta–Nyström methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge–Kutta–Nyström methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.
AB - In the paper explicit functional continuous Runge–Kutta and Runge–Kutta–Nyström methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge–Kutta–Nyström methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.
KW - Continuous Runge–Kutta
KW - Delay differential equations
KW - Functional differential equations
KW - Overlapping
KW - NUMERICAL-SOLUTION
KW - Continuous Runge-Kutta
UR - http://www.scopus.com/inward/record.url?scp=85068882589&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/functional-continuous-rungekutta-methods-reuse
U2 - 10.1016/j.apnum.2019.07.012
DO - 10.1016/j.apnum.2019.07.012
M3 - Article
AN - SCOPUS:85068882589
VL - 146
SP - 165
EP - 181
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -
ID: 43756490