A method for solving the Cauchy problem for Duffng type integro-differential equation
Mynbayeva S.
2025American Institute of Mathematical Sciences
AIMS Mathematics
2025#10Issue 614071 - 14087 pp.
The paper explored the applicability of the Dzhumabaev parametrization method to Cauchy problems with nonlinear integrodifferential operator equation arising in applied mathematics. The proposed method reformulated the problem under consideration as an equivalent parametric multipoint problem. Subsequently, linearization of the problem and stepwise solution of a sequence of linear approximations was used to solve the parametric problem. Particular emphasis was placed on solving the nonlinear special Cauchy problem for Fredholm integrodifferential equations. A novel strategy was employed to determine solutions of the original problem through this approach. The effectiveness of the proposed approach was demonstrated by numerical examples.
algorithm , Duffing type integro-differential equation, Dzhumabaev parametrization method , initial guess solution , iterative process , special Cauchy problem
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Institute of Mathematics and Mathematical Modeling, 28 Shevchenko Str, A26G7T5, Almaty, 050000, Kazakhstan
K. Zhubanov Aktobe Regional University, 34 Moldagulova Ave, Aktobe, 030000, Kazakhstan
Institute of Mathematics and Mathematical Modeling
K. Zhubanov Aktobe Regional University
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