The Time-Fractional Coupled-Korteweg-de-Vries Equations by Abdon Atangana, Aydin Secer

“…It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).…”
Get full text

A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach by Nabaraj Adhikari, Wutiphol Sintunavarat

“…The paper also examines how variations in the parameters of the iterative methods impact the resulting sets’ characteristics, such as shape, size, symmetry, and color.…”
Get full text

A note on computing the generalized inverse A T,S (2) of a matrix A by Xiezhang Li, Yimin Wei

“…In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. …”
Get full text

Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. by Nzabonimpa, Godfrey

“…Some of which are direct methods and others are iterative methods. In this work, we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. …”
Get full text

A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. by Niringiye, Richard

“…There are several methods of solving a system of linear equations,. some of which are direct methods and others are iterative methods. In this work, .we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. …”
Get full text

A Numerical Approach for the Analytical Solution of Multidimensional Wave Problems by Jinxing Liu, Jiahua Fang, Muhammad Nadeem, Yahya Alsayyad

“…Since the variational iteration method (VIM) has some assumptions and restrictions of variables during the construction of the recurrence relation, we present a Sawi integral transform for the construction of the recurrence to overcome this difficulty. …”
Get full text

Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme by Muhammad Nadeem, Hanan A. Wahash

“…Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. …”
Get full text

A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order by F. Soleymani, S. Karimi Vanani, M. Jamali Paghaleh

“…Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation per full iteration, which is important in engineering problems. …”
Get full text

Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations by Khaled A. Gepreel, Taher A. Nofal, Fawziah M. Alotaibi

“…We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. …”
Get full text

Two New Efficient Iterative Regularization Methods for Image Restoration Problems by Chao Zhao, Ting-Zhu Huang, Xi-Le Zhao, Liang-Jian Deng

“…The IDR(s) and LSMR methods are state-of-the-arts iterative methods for solving large linear systems. Recently, they have attracted considerable attention. …”
Get full text

Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems by Norhashidah Hj. Mohd Ali, Abdulkafi Mohammed Saeed

“…The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated (skewed) finite difference approximations has been shown to improve the convergence rates of these methods. …”
Get full text

Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions by Bashar Zogheib, Emran Tohidi, Stanford Shateyi

“…., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of differentiation are implemented for speeding up the operations. …”
Get full text

Convergence Analysis of New Construction Explicit Methods for Solving Equilibrium Programming and Fixed Point Problems by Chainarong Khunpanuk, Nuttapol Pakkaranang, Bancha Panyanak

“…In this paper, we present improved iterative methods for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz-type bifunction. …”
Get full text

A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics by Saima Akram, Faiza Akram, Moin-ud-Din Junjua, Misbah Arshad, Tariq Afzal

“…In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. …”
Get full text

Application of Radial Basis Function Method for Solving Nonlinear Integral Equations by Huaiqing Zhang, Yu Chen, Chunxian Guo, Zhihong Fu

“…Finally, the coefficients of RBFs were determined by Newton’s iteration method and an approximate solution was obtained. …”
Get full text

A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems by Wei-Hua Luo, Ting-Zhu Huang

“…Consequently, this can lead to a good convergence when some GMRES iterative methods are used in Krylov subspace. Numerical results of Stokes problems and Oseen problems are presented to illustrate the behavior of the preconditioner.…”
Get full text

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations by Ling Li, Yongxian Li

“…The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. …”
Get full text

GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography by Martin Schweiger

“…The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. …”
Get full text

Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering by M. A. Rehman, Amir Naseem, Thabet Abdeljawad

“…These problems also include some real-life applications associated with the chemical and civil engineering such as adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia, the van der Wall’s equation, and the open channel flow problem whose numerical results prove the better efficiency of these methods as compared to other well-known existing iterative methods of the same kind.…”
Get full text

Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation by Javad Alinejad, Sina Samarbakhsh

“…The obtained equations, including nonlinear equation for the velocity field 𝑓 and differential equation by variable coefficient for the temperature field 𝜃, are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. The effect of various values of Prandtl number, Eckert number and nonlinear stretching parameter are studied. …”
Get full text