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  • Open Access


    Computational Methods for Non-Linear Equations with Some Real-World Applications and Their Graphical Analysis

    Amir Naseem1, M.A. Rehman1, Thabet Abdeljawad2,3,4,*

    Intelligent Automation & Soft Computing, Vol.30, No.3, pp. 805-819, 2021, DOI:10.32604/iasc.2021.019164

    Abstract In this article, we propose some novel computational methods in the form of iteration schemes for computing the roots of non-linear scalar equations in a new way. The construction of these iteration schemes is purely based on exponential series expansion. The convergence criterion of the suggested schemes is also given and certified that the newly developed iteration schemes possess quartic convergence order. To analyze the suggested schemes numerically, several test examples have been given and then solved. These examples also include some real-world problems such as van der Wall’s equation, Plank’s radiation law and kinetic problem equation whose numerical results… More >

  • Open Access


    On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

    Mudassir Shams1,*, Naila Rafiq2, Nazir Ahmad Mir1,2, Babar Ahmad3, Saqib Abbasi1, Mutee-Ur-Rehman Kayani1

    Computer Systems Science and Engineering, Vol.36, No.3, pp. 493-507, 2021, DOI:10.32604/csse.2021.014476

    Abstract In this research article, we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously. These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3. Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3. Using computer algebra system Mathematica, we find the lower bound of the convergence order and verify it theoretically. Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB (R2011b), to present the global convergence properties of inverse simultaneous iterative… More >

  • Open Access


    Computer Methodologies for the Comparison of Some Efficient Derivative Free Simultaneous Iterative Methods for Finding Roots of Non-Linear Equations

    Yuming Chu1, Naila Rafiq2, Mudassir Shams3,*, Saima Akram4, Nazir Ahmad Mir3, Humaira Kalsoom5

    CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 275-290, 2021, DOI:10.32604/cmc.2020.011907

    Abstract In this article, we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations. Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine. Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes, numerical experiments and CPU time-methodology. Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous… More >

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