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Taylor-Galerkin method for solving higher-order nonlinear complex differential equations [PDF]

MethodsX
The Galerkin approach for numerically resolving higher-order Complex Differential Equations (CDEs) in a rectangular domain in the complex plane is presented in this work. Taylor polynomial functions are used in this method as basis or weighted functions.
Md. Humayun Kabir, Md. Shafiqul Islam, Md. Kamrujjaman   +2 more
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Three complex differential-difference equations

Partial Differential Equations in Applied Mathematics, 2022
In this paper, we propose three complex differential-difference equations related to the integrable differential-difference equations.
Hasi Gegen, Xing-Biao Hu
doaj   +1 more source

Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method

Complexity, 2023
In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations.
Mehmet Merdan, Merve Merdan, Rıdvan Şahin   +2 more
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On Complex Differential-Difference Equations of Malmquist Type

Journal of Mathematics, 2022
In this paper, we shall give some properties of complex differential-difference equation of the form ∑μ=1nαμz∏i=1tfz+ciai0μf′z+ciai1μ⋯fkiz+ciaikiμ/∑ν=1mβνz∏i=1tfz+cibi0νf′z+cibi1ν⋯fkiz+cibikiν=Rz,fz, where aijμ μ=1,2,…,n and bijνν=1,2,…,mi=1,2,…,t;j=0,1,…
Jianjun Zhang
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A new analytic solution of complex Langevin differential equations [PDF]

Arab Journal of Mathematical Sciences, 2023
Purpose – In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory.
Rabha W. Ibrahim
doaj   +1 more source

On the Exact Solutions of Two (3+1)-Dimensional Nonlinear Differential Equations

Journal of Function Spaces, 2020
In this article, exact solutions of two (3+1)-dimensional nonlinear differential equations are derived by using the complex method. We change the (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and generalized shallow water (gSW) equation ...
Fanning Meng, Yongyi Gu
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Data-driven and physical-based identification of partial differential equations for multivariable system

Theoretical and Applied Mechanics Letters, 2022
Data-driven partial differential equation identification is a potential breakthrough to solve the lack of physical equations in complex dynamic systems.
Wenbo Cao, Weiwei Zhang
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Solving Higher Orders Linear Complex Partial Differential Equations via Two Dimensional Differential Transform Method [PDF]

مجلة جامعة الانبار للعلوم الصرفة
Complex partial differential equation (CPDEs( appeared around the year 1900. D. Pompeiu was a famous mathematician who left a large impact in this field through introducing the Pompeiu integral operator, which forms a basis in the subject CDEs.
Amal Alhassan, Radhi Ali Zaboon, Shatha Alhily   +2 more
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Limit Directions of Julia Sets of Entire Functions and Complex Differential Equations

Journal of Mathematics, 2023
The limiting directions of Julia sets of infinite order entire functions are studied by combining the theory of complex dynamic system and the theory of complex differential equations, in which the lower bound of the measure of limiting direction of ...
Zhigao Qin, Jianren Long, Xuxu Xiang
doaj   +1 more source

Malmquist-type theorems on some complex differential-difference equations

Open Mathematics, 2022
This article is devoted to study the existence conditions of solutions to several complex differential-difference equations. We obtain some Malmquist theorems related to complex differential-difference equations with a more general form than the previous
Xu Hong Yan, Li Hong, Yu Meiying
doaj   +1 more source