Related papers: On computing differential transform of nonlinear n…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
The differential transformation method (DTM) enables the easy construction of a power-series solution to a nonlinear differential equation. The exponentiation operation has not been specifically addressed in the DTM literature, and…
In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…
In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…