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Solutions of Stiff Systems of Ordinary Differential Equations Using Residual Power Series Method

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  • Mubashir Qayyum
  • Qursam Fatima

Abstract

The stiff differential equations occur in almost every field of science. These systems encounter in mathematical biology, chemical reactions and diffusion process, electrical circuits, meteorology, mechanics, and vibrations. Analyzing and predicting such systems with conventional numerical techniques require more time and memory; still accurate solution is completely uneconomical and uncertain. Most of the numerical techniques have stability issues while dealing with stiff systems. To overcome these limitations, residual power series method (RPSM) is proposed for stiff systems of differential equations (DEs). RPSM is applied to various linear and nonlinear stiff systems, and closed‐form solutions are achieved. This indicates the effectiveness of proposed scheme for stiff family of DEs. Since this method leads to better results with less computational cost, it can be extended for more complex systems which arise in different areas of engineering and sciences.

Suggested Citation

  • Mubashir Qayyum & Qursam Fatima, 2022. "Solutions of Stiff Systems of Ordinary Differential Equations Using Residual Power Series Method," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7887136
    DOI: 10.1155/2022/7887136
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    References listed on IDEAS

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    1. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    2. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane‐Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Abd-Allah Hyder & Ahmed H. Soliman & Clemente Cesarano & M. A. Barakat, 2021. "Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
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    1. Mubashir Qayyum & Amna Khan, 2022. "Constructing and Predicting Solutions for Different Families of Partial Differential Equations: A Reliable Algorithm," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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