Figure 2 - uploaded by Jayakumar Jayaraman
Content may be subject to copyright.
Variation of θ for 2-D Bratu Problem Equation (30) is discretized using the finite-difference five-point formula with mesh length h on both the axes to obtain the nonlinear equations F(U i,j ) = −(4U i,j − λh 2 exp(U i,j )) + U i+1,j + U i−1,j + U i,j+1 + U i,j−1 , (36)
Source publication
This manuscript presents a new two-step weighted Newton's algorithm with convergence order five for approximating solutions of system of nonlinear equations. This algorithm needs evaluation of two vector functions and two Frechet derivatives per iteration. Furthermore, it is improved into a general multi-step algorithm with one more vector function...
Context in source publication
Similar publications
Finite element approximation to a decoupled formulation for the quad-curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad–curl problems has been greatly reduced. For convex domains, where the regularity assumption holds for Stokes equation, the approximation to the curl of the true solut...
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large sparse matrix exponential as it requires greater memories and computational cost than is actually needed. By in...
Error analysis is considered as a significant part in second and foreign language teaching. It helps teachers in understanding the better approaches for instructing by giving the input on the errors produced by students because students can learn from their errors. This study aimed at analyzing the errors produced by students in using do/does, have...
Microwave holography utilizes an antenna to record the hologram. In a phase shifting microwave holographic method, the antenna has to perform the 2D scanning over an area corresponding to each phase shift in reference wave. Since this methodology requires phase shifting in each scan, this makes the process lengthy and laborious. In this work, a num...
In this paper, we analyze the end-to-end (e2e) performance of a millimeter-wave (mmWave) multi-hop relay network. The relays in it are decode-and-forward (DF) type. As appropriate for mmWave bands, we incorporate path loss and blockages considering the links to be either line of sight (LOS) or non line of sight (NLOS). The links also experience Nak...
Citations
... In the last decade, many three-step iterative methods with parameters have been developed to improve the order of convergence of Newton's method. See, for example, Abbasbandy et al. [2016], Bahl et al. [2019], Behl et al. [2019b;2022], Behl and Arora [2020], Chun and Neta [2019b], Cordero et al. [2010;, Hueso et al. [2015], Kansal et al. [2021], Lotfi et al. [2015], Madhu et al. [2017], Montazeri et al. [2012], Narang et al. [2016], Sharma and Gupta [2014], Sharma and Arora [2017], Sivakumar and Jayaraman [2019], Soleymani et al. [2014], Wang et al. [2011], Wang and Li [2017], Zhanlav et al. [2017;, , and the references therein. In each of them, the authors introduced parameters in various ways based on their own experience. ...
In this paper, we derive new multi-parametric families of iterative methods whose orders range from six to eight, for solving nonlinear systems. Based on a generating function method known in the literature, we construct these families in the most general way possible in order to include some well-known methods as special cases. Several applied problems are solved to check the performance of our methods and other existing ones and to verify the theoretical results. It is found that our methods are competitive in performance compared to the other methods. Moreover, the basin of attraction method is introduced for nonlinear systems to confirm our findings and to choose the best performers.
... In Eqs. (14) and (15), X best represents the best degree of the adaptation. Therefore, X best shows the best-adapted candidate solution. ...
In this research, we have suggested a combined strategy to calculate and determine the solutions for problems originating in combustion theory and heat transfer. We know these problems as Bratu differential equations. We aim to suggest and test a soft computing technique using an efficient meta-heuristic the Symbiotic organism search (SOS) algorithm and Artificial neural network (ANN) architecture to obtain better solutions for Bratu differential equations by utilizing fewer computational resources and minimal time. We have simulated our computing approach for different6cases, and we compare the outcome of our experiments with solutions obtained by the existing state-of-the-art methods. For novelty, we have found an accurate critical value of λc by using SOS algorithm. Values of TIC, MAD, and NSE confirm that our method is a convenient and potential candidate for handling real-application problems. We discovered that our ANN-SOS algorithm takes less time and is accurate in getting results of the expected standard.
In this paper, a class of efficient iterative methods with increasing order of convergence for solving systems of nonlinear equations is developed and analyzed. The methodology uses well-known third-order Potra–Pták iteration in the first step and Newton-like iterations in the subsequent steps. Novelty of the methods is the increase in convergence order by an amount three per step at the cost of only one additional function evaluation. In addition, the algorithm uses a single inverse operator in each iteration, which makes it computationally more efficient and attractive. Local convergence is studied in the more general setting of a Banach space under suitable assumptions. Theoretical results of convergence and computational efficiency are verified through numerical experimentation. Comparison of numerical results indicates that the developed algorithms outperform the other similar algorithms available in the literature, particularly when applied to solve the large systems of equations. The basins of attraction of some of the existing methods along with the proposed method are given to exhibit their performance.
