Related papers: Iterative Methods for Solving Fourth and Sixth Ord…
In this paper, we analyze a substructuring type algorithm for the Cahn-Hilliard (CH) equation. Being a nonlinear equation, it is of great importance to develop efficient numerical schemes for investigating the solution behaviour of the CH…
In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively…
In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…
This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $\varphi$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the…
The study of long-term dynamics for numerical solutions of nonlinear evolution equations, particularly phase field models, has consistently garnered considerable attention. The Cahn-Hilliard (CH) equation is one of the most important phase…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional…
This paper concerns with a mathematical modelling of biological experiments, and its influence on our lives. Fractional hybrid iterative differential equations are equations that interested in mathematical model of biology. Our technique is…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…
High-frequency issues have been remarkably challenges in numerical methods for partial differential equations. In this paper, a learning based numerical method (LbNM) is proposed for Helmholtz equation with high frequency. The main novelty…
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the…
The object of the present work is to present the new classes of third-order and fourth-order iterative methods for solving nonlinear equations. Our third-order method includes methods of Weerakoon \cite{Weerakoon}, Homeier \cite{Homeier2},…
In this article, we discuss sixth-order and seventh-order iterative methods for nonlinear equations. Derivative-based and derivative-free, both categories are presented for said iterative methods. Especially sixth-order derivative-based and…