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AUTHOR(S): M. N. Imanova, V. R. Ibrahimov
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ABSTRACT One of the most popular problems in the investigation different questions from the Natural know ledge are reduce to solve the initial-value problem for Ordinary Differential Equations Among them are frequently encountered tasks are the initial-value problems for Ordinary Differential Equations of the first and second order. Note that, recently many works has been done on the topic of studying the Ordinary Differential Equations of second order with special structure. By using of this, many specialists have constructed different methods for solving above noted problem. Among them, the most frequently used are the Multistep Secondderivative Methods of Stormer type, which has investigated by many authors. Scientists have proven that this method does not have high accuracy. For the constructed more exact methods of Stormer type, here suggested to use advanced (forward-jumping) methods. Moreover, have given some ways for the construction more exact Multistep secondderivative Methods of advanced type. Proposed special method for finding the value of the coefficients of specified methods by using the method of unknown coefficients. For the illustration of this, here has constructed concurred methods, which have applied to solve some model problem. Here have constructed some methods of hybrid types and it is proven stat these methods are more exact, than the others. |
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KEYWORDS Initial-value problem for ODEs, Stability and Degree, Multistep Multiderivative Methods (MMM), Local Truncation Error, Störmer Method, Multistep Secondderivative Methods (MSM) |
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Cite this paper M. N. Imanova, V. R. Ibrahimov. (2025) Comparison Multistep Methods with the Multistep Secondderivative Methods and Application them to solve Ordinary Differential Equation of first and second order. International Journal of Mathematical and Computational Methods, 10, 1-10 |
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