A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations
H. M. Srivastava, Javed Iqbal, Muhammad Arif, Alamgir Khan, Yusif S. Gasimov, Ronnason Chinram
Abstract
In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with n=3). The proposed method solves nonlinear boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations.
Topics & Concepts
Nonlinear systemGaussian quadratureQuadrature (astronomy)GaussNyström methodMathematicsApplied mathematicsConvergence (economics)Gauss–Kronrod quadrature formulaNumerical integrationIntegral equationBoundary value problemMathematical analysisComputer sciencePhysicsEconomicsOpticsQuantum mechanicsEconomic growthIterative Methods for Nonlinear EquationsFractional Differential Equations SolutionsMatrix Theory and Algorithms