We construct an optimal eighth-order scheme which will work for multiple zeros with multiplicity [Formula: see text], the first time. Earlier, maximum convergence order of multi-point iterative schemes was six in available literature. So, main contribution this study is to present a new higher-order and as well In addition, we extensive analysis theorem confirms theoretically proposed scheme. Moreover, consider several real life problems contain simple compare existing robust schemes....

A load flow study referred to as a power is numerical analysis of the electricity that flows through any electrical system. For instance, if transmission line needs be taken out service for maintenance, studies allow us assess whether remaining can carry without exceeding its rated capacity. So, we need understand about voltage level and phase angle on each bus under steady-state conditions keep within specific range. In this paper, our goal present higher order efficient iterative method...

Some new families of open Newton-Cotes rules which involve the combinations function values and evaluation derivative at uniformly spaced points interval are presented. The order accuracy these numerical formulas is higher than that classical formulas. An extensive comparison computational cost, accuracy, error terms, coefficients observed CPU usage time, results obtained from given. comparisons show we have been able to define some superior for less number nodes cost with increased accuracy.

In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots nonlinear equations with known multiplicity ( m ≥ 1 ) . We use the weight function approach involving one two parameters to develop family. A comprehensive convergence analysis is studied demonstrate eighth-order suggested scheme. Finally, numerical dynamical tests are presented, which validates theoretical results formulated in paper illustrates that among domain root methods.

Finding a repeated zero for nonlinear equation f ( x ) = 0 , : I ⊆ R → has always been of much interest and attention due to its wide applications in many fields science engineering. Modified Newton’s method is usually applied solve this kind problems. Keeping view that very few optimal higher-order convergent methods exist multiple roots, we present new family eighth-order iterative roots with known multiplicity involving multivariate weight function. The numerical performance the proposed...

We construct a family of derivative-free optimal iterative methods without memory to approximate simple zero nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable with-memory class. The extension new one also presented which attains order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mn mathvariant="normal">15.5156</mml:mn></mml:mrow></mml:math> very high efficiency index id="M2"><mml:mn...

Newton‐Raphson method has always remained as the widely used for finding simple and multiple roots of nonlinear equations. In past years, many new methods have been introduced zeros that involve use weight function in second step, thereby, increasing order convergence giving a flexibility to generate family satisfying some underlying conditions. However, almost all schemes developed over past, usual way is Newton‐type at first step. this paper, we present two‐step optimal fourth‐order ( m...

Solving systems of nonlinear equations plays a major role in engineering problems. We present new family optimal fourth-order Jarratt-type methods for solving and extend these to solve system equations. Convergence analysis is given both cases show that the order four. Cost computations, numerical tests, basins attraction are presented which illustrate as better alternates previous methods. also give an application proposed well-known Burger's equation.

We have given two general methods of converting with derivative two-step to without methods.It can also be observed that this conversion not only retain the optimal order convergence but resulting free families iterative are extendable memory class.The with-memory show greater acceleration in convergence.In way, is accelerated from 4 7.53 at most.An extensive comparison our done recent respective domain.

In this paper, some generalized Hermite-Hadamard type inequalities for n-times differentiable (ρ, m)geometrically convex function are established.The new recapture and give estimates of the previous first functions as special cases.The trapezoid, midpoint, averaged mid-point trapezoid Simpson's can also be obtained higher geometrically functions.

We construct a new general class of derivative free<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>-point iterative methods optimal order convergence<mml:math id="M2"><mml:mrow><mml:msup><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>using rational interpolant. The special cases this...

Abstract Many real-life problems using mathematical modeling can be reduced to scalar and system of nonlinear equations. In this paper, we develop a family three-step sixth-order method for solving equations by employing weight functions in the second third step scheme. Furthermore, extend multidimensional case preserving same order convergence. Moreover, have made numerical comparisons with efficient methods domain verify suitability our method.

In this paper, we have established the Hermite–Hadamard–Fejér inequality for fractional integrals involving preinvex functions. The results presented here provide new extensions of those given in earlier works as weighted estimates left and right hand side Hermite–Hadamard inequalities functions doesn’t exist previously.

In this paper, we present some new Hermite-Hadamard-Fejér type inequality for fractional integrals (η 1 , η 2 )-convex functions.Our results give error bounds the weighted trapezoidal and midpoint rules in domain.The presented here are noteworthy extensions of earlier works.

&lt;abstract&gt;&lt;p&gt;The problem of solving a nonlinear equation is considered to be one the significant domain. Motivated by requirement achieve more optimal derivative-free schemes, we present an eighth-order method find multiple zeros weight function approach in this paper. This family methods requires four functional evaluations. The technique based on three-step including first step as Traub-Steffensen iteration and next two Traub-Steffensen-like iterations. Our proposed scheme...

The global positioning system (GPS) is a satellite navigation that determines locations. Whenever the baseline satellites are serviced or deactivated, Space Force often flies more than 24 GPS to maintain coverage. additional not regarded as part of core constellation but may improve performance GPS. In this study models, we solved various problems. We examined each set four separately. Advancements in computer softwares have made computations much precise. can use iterative methods solve...

Finding a simple root for nonlinear equation f ( x ) = 0 , : I ⊆ R → has always been of much interest due to its wide applications in many fields science and engineering. Newton’s method is usually applied solve this kind problems. In paper, such problems, we present family optimal derivative-free finding methods arbitrary high order based on inverse interpolation modify it by using transformation first derivative. Convergence analysis the modified confirms that convergence preserved...

Abstract In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first divided difference and weight functions. This iterative method a three step with as Traub–Steffensen iteration next two taken Traub–Steffensen-like four functional evaluations per iteration. We compare our proposed recent using some chemical engineering problems modelled nonlinear equations simple roots. Stability presented demonstrated by graphical tool...

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving specific step which when combined with any two-step method raises the convergence order by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>10</mml:mn></mml:math>, if id="M2"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math> is method. This new class include four evaluations function and one evaluation first derivative per...

In this paper, we study generalized definitions of left and right conformable fractional derivative integrals. Some applications the definition are also given for nonlinear differential equations. We establish identities associated with left‐ right‐hand side Hermite–Hadamard–Fejér inequality preinvex functions. We, then, give some new bounds inequalities functions using