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Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem

Author

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  • Mariusz Pleszczyński

    (Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland)

  • Konrad Kaczmarek

    (Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland)

  • Damian Słota

    (Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland)

Abstract

The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms: Different Transform Method (DTM) and Adomian Decomposition Method (ADM). The combination of these two methods resulted in a continuous approximate solution to this problem and eliminated the problems that occur when trying to use each of these methods separately. The great advantages of the DTM method are the continuous form of the solution and the fact that it easy to implement error control. However, in too-complex tasks, this method becomes difficult to use. By using a hybrid of ADM and DTM, we obtain a relatively simple-to-implement method that retains the advantages of the DTM approach.

Suggested Citation

  • Mariusz Pleszczyński & Konrad Kaczmarek & Damian Słota, 2024. "Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem," Mathematics, MDPI, vol. 12(23), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3858-:d:1539003
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    References listed on IDEAS

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    1. Edyta Hetmaniok & Mariusz Pleszczyński, 2022. "Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    2. Rumen L. Mishkov, 2000. "Generalization of the formula of Faa di Bruno for a composite function with a vector argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
    3. Mehmet Merdan & Ahmet Gökdoğan & Ahmet Yıldırım & Syed Tauseef Mohyud-Din, 2012. "Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, February.
    4. Mohammad Izadi & Şuayip Yüzbaşi & Samad Noeiaghdam, 2021. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    5. Rafał Brociek & Mariusz Pleszczyński, 2024. "Differential Transform Method and Neural Network for Solving Variational Calculus Problems," Mathematics, MDPI, vol. 12(14), pages 1-13, July.
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