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  • Open Access


    Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

    Xuechuan Wang1, Wei He1,*, Haoyang Feng1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1263-1294, 2024, DOI:10.32604/cmes.2023.043068

    Abstract Although predictor-corrector methods have been extensively applied, they might not meet the requirements of practical applications and engineering tasks, particularly when high accuracy and efficiency are necessary. A novel class of correctors based on feedback-accelerated Picard iteration (FAPI) is proposed to further enhance computational performance. With optimal feedback terms that do not require inversion of matrices, significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts; however, the computational complexities are comparably low. These advantages enable nonlinear engineering problems to be solved quickly and accurately, even with rough initial guesses from elementary predictors.… More > Graphic Abstract

    Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

  • Open Access


    A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory

    Pushpendra Kumar1,*, Vedat Suat Erturk2, V. Govindaraj1, Dumitru Baleanu3,4,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2487-2506, 2023, DOI:10.32604/cmes.2023.026009

    Abstract In this article, we introduce a nonlinear Caputo-type snakebite envenoming model with memory. The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractional-order sense. The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector (L1-PC) scheme with error estimation and stability analysis. The proof of the existence and positivity of the solution is given by using the fixed point theory. From the necessary simulations, we justify that the first-time implementation of the proposed method on an epidemic model shows that the scheme is fully suitable and time-efficient… More >

  • Open Access


    Fractional-Order Model for Multi-Drug Antimicrobial Resistance

    M. F. Elettreby1, 2, *, Ali S. Alqahtani1, E. Ahmed2

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 665-682, 2020, DOI:10.32604/cmes.2020.09194

    Abstract Drug resistance is one of the most serious phenomena in financial, economic and medical terms. The present paper proposes and investigates a simple mathematical fractional-order model for the phenomenon of multi-drug antimicrobial resistance. The model describes the dynamics of the susceptible and three kinds of infected populations. The first class of the infected society responds to the first antimicrobial drug but resists to the second one. The second infected individuals react to the second antimicrobial drug but resist to the first one. The third class shows resistance to both of the two drugs. We formulate the model and associate it… More >

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