Quadrature Rule Based Iterative Method for the Solution of Non-Linear Equations
Quadrature Rule for the Solution of Non-Linear Equations
Keywords:
Nonlinear problems, Second order method, Quadrature formula, Convergence analysis, ErrorAbstract
This research has suggested a quadrature rule based iterative method for the solution of non-linear algebraic and transcendental equations. The proposed iterated method is derived from Quadrature Formula and Numerical Technique. The quadrature rule based iterative method is converged quadratically, and it is free from pitfall. Few of physical non-linear problems to demonstrate the competency of proposed iterative method with the assessment of Steffensen Method and Newton Raphson Method. C++ and EXCEL have been used to examine the numerical results and graphical illustration of quadrature rule based iterative method. Hence, from several examples illustrate that the convergence and efficiency of the quadrature rule based iterative method is better than Steffensen Method and Newton Raphson Method.
References
Biswa. N. D. Lecture Notes on Numerical Solution of root Finding Problems. 1-40 (2012).
François Dubeau. On Corrected Quadrature Rules and Optimal Error Bounds. Abstract and Applied Analysis. Vol. 2015.
Qureshi,U. K., Z. A. Kalhoro, A. A. Shaikh & A. R. Nagraj. Trapezoidal Second Order Iterated Method for Solving Nonlinear Problems. 2(2): 31-34 (2018).
Ahmad, N., & V. P. Singh. A New Iterative Method for Solving Nonlinear Equations Using Simpson Method. 5(4): 189–193 (2017).
Qureshi. U. K. A New Accelerated Third-Order Two-Step Iterative Method for Solving Nonlinear Equations. Mathematical Theory and Modeling. 8(5): 64-68 (2018).
Eskandari. H. Simpson’s Method for Solution of Nonlinear Equation. International Journal of Applied Mathematics and Engineering Sciences. Applied Mathematics. 8(1): 929-933 (2017).
Frontini, M., & E. Sormani. Third-order methods from quadrature formulae for solving systems of nonlinear equations. Applied Mathematics and Computation. 149(1): 771–782(2004).
Qureshi, U. K., A. A. Shaikh & P. K. Malhi. Modied Bracketing Method for Solving Nonlinear Problems with Second Order of Convergence. Punjab Univ. j.Math. 50(3): 145-151(2018).
Singh, A. K., M. Kumar & A. Srivastava. A New Fifth Order Derivative Free Newton-Type Method for Solving Nonlinear Equations.Applied Mathematics & Information Sciences an International Journal. 9(3): 1507-1513 (2015).
Rafiq, A., S. M. Kang & Y. C. Kwun. A New Second- Order Iteration Method for Solving Nonlinear Equations.Hindawi Publishing Corporation Abstract and Applied Analysis. (2013).
Qureshi, U. K., A. A. Shaikh & M. A. Solangi. Modified Free Derivative Open Method for Solving Non-Linear Equations. Sindh University Research Journal. 49(4): 821-824 (2017).
Cordero. A., L. José., E. Martínez & R.T. Juan .Steffensen type methods for solving nonlinear equations. Journal of Computational and Applied Mathematics. 236: 3058–3064 (2012).
