Cubic Iterated Methods of Numerical Differential Method for Solving Non-Linear Physical Functions

Authors

  • Umair Khalid Qureshi Department of Business Administration, Shaheed Benazir Bhutto University, Sanghar Campus, Sindh, Pakistan
  • Muzaffar B. Aarain Department of Mathematics and Statistics, Quaid-e-Awam, University of Engineering, Science and Technology, Nawabshah, Pakistan
  • Rahim Bux Khokhar Department of Basic Science and Related Studies, Mehran University Engineering and Technology, Jamshoro, Sindh, Pakistan
  • Manzar Bashir Department of Information Technology, Shaheed Benazir Bhutto University, Sanghar Campus, Sindh, Pakistan

DOI:

https://doi.org/10.21015/vtm.v11i1.1420

Abstract

In this research two iterated methods have been developed for solving non-linear equations, which arises in applied sciences and engineering. The proposed iterated methods are converged cubically, and it is derived from modified euler method and improved euler method with steffensen method. The cubic iterated methods of numerical differential method are work on physical application functions and compared with variant newton iterated method. The numerical outcome of proposed cubic iterated methods of numerical differential method is examined with C++/MATLAB. From the numerical results, it can be observed that the cubic iterated methods of numerical differential method are good for accuracy point of view, iteration perception and function evaluation as the assessment of variant newton iterated method for solving non-linear physical functions.

References

Abassy, T. A., El-Tawil, M. A. and El-Zoheiry, H. [2007], ‘Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with laplace transforms and the padé technique’, Computers & Mathematics with Applications 54(7-8), 940–954.

Aliya, T., Shaikh, A. A. and Qureshi, S. [2018], ‘Development of a nonlinear hybrid numerical method’, Advances in Differential Equations and Control Processes 19(3), 275–285.

Ansari, M. Y., Shaikh, A. A. and Qureshi, S. [2018], ‘Error bounds for a numerical scheme with reduced slope evaluations’, J. Appl. Enviro. Biolog. Sci 8, 67–76.

Khatri, A., Shaikh, A. and Abro, K. [2019], ‘Closed newton cotes quadrature rules with deriatives’, Mathematical Theory and Modeling 9(5), 65–72.

Muriel, C. and Romero, J. [2009], ‘First integrals, integrating factors and λ-symmetries of second-order differential equations’, Journal of Physics A: Mathematical and Theoretical 42(36), 365207.

PERHIYAR, M. A., SHAH, S. F. and Shaikh, A. [n.d.], ‘Modified trapezoidal rule based different averages for numerical integration’.

Polyanin, A. D. [2019], ‘Functional separable solutions of nonlinear reaction–diffusion equations with variable coefficients’, Applied Mathematics and Computation 347, 282–292.

Qureshi, U. K., Bozdar, I. A., Pirzada, A. and Arain, M. B. [2019], ‘Quadrature rule based iterative method for the solution of non-linear equations’, Proceedings of the Pakistan Academy of Sciences, Pakistan Academy of Sciences A. Physical and Computational Sciences 56(1), 39–43.

Qureshi, U. K., Jamali, S., Kalhoro, Z. A. and Shaikh, A. G. [2021], ‘Modified quadrature iterated methods of boole rule and weddle rule for solving non-linear equations’, Journal of Mechanics of continua and Mathematical sciences 16(2), 87–101.

Qureshi, U. K., Kalhoro, Z. A., Shaikh, A. A. and Nangraj, A. R. [2018], ‘Trapezoidal second order convergencemethodfor

solving nonlinear problems’, University of Sindh Journal of Information and Communication Technology 2(2), 111–114.

Qureshi, U. K. and UK, A. [2018], ‘A new accelerated third-order two-step iterative method for solving nonlinear equations’, Mathematical Theory and Modeling 8(5), 64–68.

Qureshi, U., Shaikhi, A., Shaikh, F., Hazarewal, S. and Laghari, T. [2021], ‘New simpson type method for solving nonlinear equations’, Open J. Math. Sci 5, 94–100.

Shaikh, M., Chandio, M. and Soomro, A. [2016], ‘A modified four-point closed mid-point derivative based quadrature rule for numerical integration’, Sindh University Research Journal-SURJ (Science Series) 48(2), 389–392.

Weerakoon, S. and Fernando, T. [2000], ‘A variant of newton’s method with accelerated third-order convergence’, Applied mathematics letters 13(8), 87–93.

Zafar, F., Saleem, S. and Burg, C. O. [2014], New derivative based open newton-cotes quadrature rules, in ‘Abstract and Applied Analysis’, Vol. 2014, Hindawi.

Zhao, W. and Li, H. [2013], Midpoint derivative-based closed newton-cotes quadrature, in ‘Abstract and Applied Analysis’, Vol. 2013, Hindawi.

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Published

2023-04-13