The convergence order of higher-order iterative methods for solving systems of nonlinear equations was analyzed using Taylor series expansion, which typically requires the computation of higher-order derivatives not inherently part of the method. Thi...
In this paper, a localized boundary knot method is adopted to solve two-dimensional inverse Cauchy problems, which are controlled by a second-order linear differential equation. The localized boundary knot method is a numerical method based on the lo...
In connection with applications, the solution of a system of logical equations plays an important role in computational mathematics and in many other areas. As a result, many new directions and algorithms for solving systems of logical equations are...
The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics an...
We present an improved version of the Hănțilă Method (HM) for circuits with multiple nonlinear resistive elements (NRCEs). The method replaces NRCEs with generators consisting of linear resistors and nonlinear controlled sources, whose...
In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differenti...
In this paper, we propose a neural network method to solve time-fractional diffusion equations with Dirichlet boundary conditions by using a combination of machine learning techniques and Method of Lines. We first used the Method of Lines to discreti...
In this article, we examine the use of symmetry groups for modeling applied problems through computer symbolic calculus. We consider the problem of solving radical equations symbolically using computer mathematical packages. We propose some methods t...
In this paper we propose a parallel two-stage iteration algorithm for solving large-scale continuous Sylvester equations. By splitting the coefficient matrices, the original linear system is transformed into a symmetric linear system which is then so...
The most popular iterative methods for solving nonsymmetric linear systems are Krylov methods. Recently, an optimal Quasi-ORthogonal (Q-OR) method was introduced, which yields the same residual norms as the Generalized Minimum Residual (GMRES) method...
In this paper, we use the ARA transform to solve families of fractional differential equations. New formulas about the ARA transform are presented and implemented in solving some applications. New results related to the ARA integral transform of the...
In this paper, an efficient numerical method is presented for solving the generalized time-fractional Boussinesq equation. The Caputo fractional derivative is approximated by the
In this study, a novel space-time (ST) marching method is presented to solve linear and nonlinear transient flow problems in porous media. The method divides the ST domain into subdomains along the time axis. The solutions are approximated using ST p...
This paper aims to develop a meshless radial point interpolation (RPI) method for obtaining the numerical solution of fractional Navier–Stokes equations. The proposed RPI method discretizes differential equations into highly nonlinear algebraic...
The bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korp...
In this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Cap...
The localized method of fundamental solutions (LMFS) is a domain-type, meshless numerical method. Compared with numerical methods that have a high grid dependence, it does not require grid generation and numerical integration, so it can effectively i...
In this paper, a new multi-parameter iterative algorithm is proposed to address the PageRank problem based on the multi-splitting iteration method. The proposed method solves two linear subsystems at each iteration by splitting the coefficient matrix...
This article presents an inexact optimal hybrid conjugate gradient (CG) method for solving symmetric nonlinear systems. The method is a convex combination of the optimal Dai–Liao (DL) and the extended three-term Polak–Ribiére–Polyak (PRP) CG methods....
Inverse problems for a 3D model of electrostatics, which arise when developing technologies for designing electric cloaking and shielding devices, are studied. It is assumed that the devices being designed to consist of a finite number of concentric...
Recently, a lot of attention has been paid to the field of research connected with the wireless sensor network and industrial internet of things. The solutions found by theorists are next used in practice in such area as smart industries, smart devic...
We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. Th...
A local and a semi-local convergence analysis are presented for the Kurchatov-type method to solve numerically nonlinear equations in a Banach space. The method depends on a real parameter. By specializing the parameter, we obtain methods already stu...
In this article we have developed a new explicit four-step linear method of fourth algebraic order with vanished phase-lag and its first derivative. The efficiency of the method is tested by solving effectively the one-dimensional time independent Sc...
In this paper, by equivalently reformulating the absolute value equation (AVE) into an alternative two-by-two block nonlinear equation, we put forward an alternative SOR-like (ASOR-like) iteration method to solve the AVE. The convergence of the ASOR-...
This paper is devoted to the wavelet Galerkin method to solve the Fractional Riccati equation. To this end, biorthogonal Hermite cubic Spline scaling bases and their properties are introduced, and the fractional integral is represented based on these...
In this article, modified techniques, namely the variational iteration transform and Shehu decomposition method, are implemented to achieve an approximate analytical solution for the time-fractional Fornberg–Whitham equation. A comparison is ma...
In this paper, we use the modified decomposition method for solving the system of third-order nonlinear boundary value problems associated with obstacle problems. Some examples of system of third-order nonlinear boundary value problems are given. The...
The main focus in this manuscript is to find a numerical solution of a dengue fever disease model by using the Fibonacci wavelet method. The operational matrix of integration has been obtained using Fibonacci wavelets. The proposed method is called F...
We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted converge...
In our paper, we present a sparse quasi-Newton method, called the sparse direct Broyden method, for solving sparse nonlinear equations. The method can be seen as a Broyden-like method and is a least change update satisfying the sparsity condition and...
Unconstrained optimization problems have a long history in computational mathematics and have been identified as being among the crucial problems in the fields of applied sciences, engineering, and management sciences. In this paper, a new variant of...
This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of...
An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs). To do this, we reduce the desired equation to an equivalent linear or nonlinear...
The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other...
Multidimensional integro-differential equations are obtained when the unknown function of several independent variable and/or its derivatives appear under an integral sign. When the differentiation or integration operators or both are of fractional o...
The physics-informed neural network (PINN) is an effective alternative method for solving differential equations that do not require grid partitioning, making it easy to implement. In this study, using automatic differentiation techniques, the PINN m...
To improve the accuracy of second-order cell-centered finite volume method in near-boundary regions for solving the two-dimensional shallow water equations, a numerical scheme with globally second-order accuracy was proposed. Having the primary objec...
In this work, an efficient algorithm is proposed for solving the system of Volterra integral equations based on wavelet Galerkin method. This problem is reduced to a set of algebraic equations using the operational matrix of integration and wavelet t...
We adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform...
Microwave heating is a process in which the electric, magnetic, and temperature fields are coupled with each other and are characterised by strong non-linearity, high time variability, and infinite dimensionality. This paper proposes a method for pre...
In many real word applications, beam has nonlinear transversely vibrations. Solving nonlinear beam systems is complicated because of the high dependency of the system variables and boundary conditions. It is important to have an accurate parametric a...
In this paper, we present an accurate numerical approach based on the reproducing kernel method (RKM) for solving second-order fuzzy initial value problems (FIVP) with symmetry coefficients such as symmetric triangles and symmetric trapezoids. Findin...
A method for accurately analyzing electrocardiograms (ECGs), which are obtained from electrical signals generated by cardiac activity, is essential in heart disease diagnosis. However, rhythms are typically obtained with relatively few data samples a...
This paper introduces an enhanced Iterative Finite Difference (IFD) method for efficiently solving strongly nonlinear, time-dependent problems. Extending the original IFD framework for nonlinear ordinary differential equations, we generalize the appr...
In this paper, a tensor splitting AOR iterative method for solving the
The method of particular solutions (MPS) has been widely applied for solving various types of partial differential equations. In this paper, the space–time collocation technique is implemented using MPS with polynomial basis functions (MPS-PBF)...
This paper proposes a localized Hermite method of approximate particular solutions (LHMAPS) for solving the 2D inhomogeneous Helmholtz-type equations. Building on the local scheme of the localized method of approximate particular solutions (LMAPS) fo...
A new two-step interior point method for solving linear programs is presented. The technique uses a convex combination of the auxiliary and central points to compute the search direction. To update the central point, we find the best value for step s...
In this paper, by using the smoothing Fischer-Burmeister function, we present a new smoothing conjugate gradient method for solving the nonlinear nonsmooth complementarity problems. The line search which we used guarantees the descent of the method....
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