A quadrature method for the numerical solution of two real nonlinear equations in two unknowns
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Ioakimidis, Nikolaos
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Abstract
A quadrature method for the numerical solution of a system of two real nonlinear equations in two unknowns in a region of the xy-plane, based on the use of two appropriate numerical integration rules for ordinary integrals in this region, is proposed. The main advantage of the method, beyond its originality and peculiarity, is the fact that no initial approximation to the sought solution is required. Three numerical applications, where the Gauss– and Lobatto–Chebyshev quadrature rules have been used, show the efficiency and the convergence of the proposed method. A generalization to the case of four real nonlinear equations in four unknowns (by using quaternions) is also suggested in brief.
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Systems of nonlinear equations, Systems of real algebraic equations, Solution of systems of equations, Noniterative methods, Approximate solutions, Numerical solutions, Numerical integration, Quadrature rules, Gauss–Chebyshev rule, Lobatto–Chebyshev rule, Quaternions