Abstract
In this paper, we present a new approach for solving fuzzy nonlinear equations. Our approach requires to compute the Jacobian matrix once throughout the iterations unlike some Newton’s-like methods which needs to compute the Jacobian matrix in every iterations. The fuzzy coefficients are presented in parametric form. Numerical results on well-known benchmarks fuzzy nonlinear equations are reported to authenticate the effectiveness and efficiency of the approach.
Highlights
Solving systems of nonlinear equations is becoming more essential state in analysis and handling complex problems in many research areas (e.g Robotics, Radiative transfer, Chemistry, Economics, e.t.c)
We present a new approach for solving fuzzy nonlinear equations
The standard analytical technique presented by [4, 10] cannot be suitable for handing the fuzzy nonlinear equations such as (i) ax3 + bx2 + cx − e = f (ii) d sin(x) − gx = h (iii) ix2 + f cos(x) = a (iv) x − cos(x) = d where, a, b, c, d, e, f, g, h, i are fuzzy numbers
Summary
Solving systems of nonlinear equations is becoming more essential state in analysis and handling complex problems in many research areas (e.g Robotics, Radiative transfer, Chemistry, Economics, e.t.c). The most widest approach to solve such nonlinear systems is Newton’s initiative [3], yet it required to compute the Jacobian matrix in every iteration. It worth to mention that, [11] has extended the approach of [9] to solve dual fuzzy nonlinear systems Their approach required to compute and store the Jacobian matrix in every iteration. A new approach via Newton’s and Broyden’s method is proposed to solve dual fuzzy nonlinear equations.
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