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Finding Solution to the Initial Value Problem for ODEs First and Second Order by One and the Same Method

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Mathematics and Computation (IACMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 418))

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Abstract

As is known by using a change of variables, the determination of the solution of ODEs of the second order can be reduced to finding the solution of the system of ODEs of the first order. Therefore, here we have considered a comparison of the multistep methods with the multistep second derivative methods. For this aim suggested here to use the advanced and hybrid methods, which are more exact than the explicit and implicit methods. Some advantages of the proposed methods here have and defined the maximum value of the degree to stable methods. Here for the comparison of these methods with the known ones have defined the disadvantages of the constructed methods and have given the way for the correction mentioned disadvantages of these methods. Constructed, specific methods, which have been applied to solve some simple problems. Note that these methods are not a special case of the known methods. Therefore these methods are independent and they constitute an independent class of methods. For the illustration of the benefits of this method, we have considered the application of some of the suggested methods here to solve some simple problems.

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Acknowledgements

The authors wishes to express their thanks to academicians Telman Aliyev and Ali Abbasov for their suggestion to investigate the computational aspects of our problem and for their frequent valuable suggestion. This work was supported by the Science Development Foundation under the President of Republic of Azerbaijan—Grant No EIF-MQM-ETS-2020-1(35)-08/01/1-M-01 (for Vagif Ibrahimov and Galina Mehdiyeva).2020–2025, Hubei ChuTian Scholar Funding, China (For Xiao-Guang Yue). The authors wishes also to thank the anonymous reviewers for their careful reading of the manuscript and their fruitful comments and suggestions.

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Authors and Affiliations

  1. Institue of Control System Named After Academician A. Huseynov, Baku, AZ1141, Azerbaijan

    V. R. Ibrahimov & M. N. Imanova

  2. Computational Mathematics, Baku State University, Baku, AZ1148, Azerbaijan

    V. R. Ibrahimov, G. Yu. Mehdiyeva & M. N. Imanova

  3. Science Development Foundation, The Republic of Azerbaijan, Baku, AZ1025, Azerbaijan

    M. N. Imanova

Authors
  1. V. R. Ibrahimov
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  2. G. Yu. Mehdiyeva
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  3. M. N. Imanova
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Corresponding author

Correspondence to V. R. Ibrahimov .

Editor information

Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Applied Mathematics, Universitat Politècnica de València, Valencia, Spain

    Juan C. Cortés

  3. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Aliaa Burqan

  4. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Ahmad Qazza

  5. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

  6. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Gharib Gharib

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Ibrahimov, V.R., Mehdiyeva, G.Y., Imanova, M.N. (2023). Finding Solution to the Initial Value Problem for ODEs First and Second Order by One and the Same Method. In: Zeidan, D., Cortés, J.C., Burqan, A., Qazza, A., Merker, J., Gharib, G. (eds) Mathematics and Computation. IACMC 2022. Springer Proceedings in Mathematics & Statistics, vol 418. Springer, Singapore. https://doi.org/10.1007/978-981-99-0447-1_28

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