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Perturbation Expansion to the Solution of Differential Equations

A Collection of Papers on Chaos Theory and Its Applications, 2020
The main purpose of this chapter is to describe the application of perturbation expansion techniques to the solution of differential equations. Approximate expressions are generated in the form of asymptotic series.
J. Mohapatra
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Multivariate hypergeometric solutions of cosmological (dS) correlators by d log-form differential equations

Journal of High Energy Physics
In this paper, we give the analytic expression for the homogeneous part of solutions of arbitrary tree-level cosmological correlators, including massive propagators and time-derivative interaction cases.
Jiaqi Chen, Bo Feng, Yi-Xiao Tao
doaj   +2 more sources

A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations [PDF]

Journal of Scientific Computing, 2023
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step procedure, defined over a graded mesh, which is based on a truncated expansion of the vector field along the orthonormal Jacobi ...
L. Brugnano, Kevin Burrage, Pamela M. Burrage, F. Iavernaro   +3 more
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Real time lattice correlation functions from differential equations [PDF]

Journal of High Energy Physics, 2023
We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation functions are calculated by the method of differential equations.
Federico Gasparotto, S. Weinzierl, Xiaofeng Xu   +2 more
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A comparative analysis of generalized and extended (G′G)-Expansion methods for travelling wave solutions of fractional Maccari's system with complex structure

Alexandria Engineering Journal, 2023
Fractional partial differential equations emerge as a prominent research area in recent times owing to their ability to depict intricate physical phenomena. Discovering travelling wave solutions for fractional partial differential equations is an arduous
Rashid Ali, Elsayed Tag-eldin
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Solutions of Nonlinear Integro-Partial Differential Equations by the Method of G′/G,1/G

Advances in Mathematical Physics, 2022
In this article, a special expansion method is implemented in solving nonlinear integro-partial differential equations of 2+1-dimensional using a special expansion method of G′/G,1/G.
Daba Meshesha Gusu, Chala Bulo
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An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

Mendel, 2022
This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations.
Werry Febrianti, Kuntjoro Adji Sidarto, Novriana Sumarti   +2 more
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Perturbed Taylor expansion for bifurcation of solution of singularly parameterized perturbed ordinary differentia equations and differential algebraic equations

Journal of Education for Pure Science- University of Thi-Qar, 2021
In This paper deals with the study of singularity perturbed ordinary differential equation, and is considered the basis for obtaining the system of differential algebraic equations.
Dr.Kamal Hamid Yasser Al-Yassery, Zahraa Hameed Ali Al-Kafaji   +1 more
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UNIFORMLY CONVERGENT NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC DIFFERENTIAL EQUATIONS ARISING IN COMPUTATIONAL NEUROSCIENCE

Kragujevac Journal of Mathematics, 2022
The motive of this work is to develop ε-uniform numerical method for solving singularly perturbed parabolic delay differential equation with small delay. To approximate the term with the delay, Taylor series expansion is used.
M. Woldaregay, G. Duressa
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Spectral analysis of the Koopman operator for partial differential equations. [PDF]

Chaos, 2020
We provide an overview of the Koopman-operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state.
H. Nakao, I. Mezić
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