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On the convergence of finite integration method for system of ordinary differential equations

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  • Soradi-Zeid, Samaneh
  • Mesrizadeh, Mehdi

Abstract

The current work investigates basic theory of finite integration method for first-order system of ordinary differential equations. We firstly investigate the error analysis of generalized finite integration methods which are constructed by ordinary linear approach. Then, the basic concepts of the error bounded theorems are discussed for a spectral meshless method derived from quadrature rule producing by radial point collocation method. By applying the finite integration methods for the first-order system of ordinary differential equation, we compare the accuracy residual error of the presented methods. The convergence of finite integration methods is proposed to confirm the standard criteria with theoretically accurate results. Finally, we extend the results for n-order system of ordinary differential equations.

Suggested Citation

  • Soradi-Zeid, Samaneh & Mesrizadeh, Mehdi, 2023. "On the convergence of finite integration method for system of ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011912
    DOI: 10.1016/j.chaos.2022.113012
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    References listed on IDEAS

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    1. Verdière, Nathalie & Manceau, David & Zhu, Shousheng & Denis-Vidal, Lilianne, 2020. "Inverse problem for a coupling model of reaction-diffusion and ordinary differential equations systems. Application to an epidemiological model," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Yun, D.F. & Wen, Z.H. & Hon, Y.C., 2015. "Adaptive least squares finite integration method for higher-dimensional singular perturbation problems with multiple boundary layers," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 232-250.
    3. Chang, Shuenn-Yih, 2022. "A family of matrix coefficient formulas for solving ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    4. Liu, Hong-Zhun, 2022. "A modification to the first integral method and its applications," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    5. Qiu, Xing & Xu, Tao & Soltanalizadeh, Babak & Wu, Hulin, 2022. "Identifiability analysis of linear ordinary differential equation systems with a single trajectory," Applied Mathematics and Computation, Elsevier, vol. 430(C).
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