A method of directly defining the inverse mapping for solutions of coupled systems of nonlinear differential equations

2017 ◽  
Vol 77 (4) ◽  
pp. 1199-1211 ◽  
Author(s):  
Mathew Baxter ◽  
Mangalagama Dewasurendra ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Coupled Systems ◽  
Inverse Mapping

scholarly journals On the Method of Inverse Mapping for Solutions of Coupled Systems of Nonlinear Differential Equations Arising in Nanofluid Flow, Heat and Mass Transfer

2018 ◽  
Vol 3 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Mangalagama Dewasurendra ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Mass Transfer ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Mapping Method ◽  
Coupled Systems ◽  
Inverse Mapping ◽  
Science And Engineering ◽  
Nanofluid Flow ◽  
Flow Heat

AbstractVery recently, Liao has invented a Directly Defining Inverse Mapping Method (MDDiM) for nonlinear differential equations. Liao’s method is novel and can be used for solving several problems arising in science and engineering, if we can extend it to nonlinear systems. Hence, in this paper, we extend Liao’s method to nonlinear-coupled systems of three differential equations. Our extension is not limited to single, double or triple equations, but can be applied to systems of any number of equations.

DIFFERENTIAL EQUATIONS FOR CUBIC THETA FUNCTIONS

2011 ◽  
Vol 07 (07) ◽  
pp. 1945-1957 ◽  
Author(s):  
TIM HUBER
Keyword(s):  
Differential Equations ◽  
Eisenstein Series ◽  
Theta Function ◽  
Modular Group ◽  
Short Proof ◽  
Nonlinear Differential Equations ◽  
Theta Functions ◽  
Coupled Systems ◽  
Function Identity ◽  
Theta Function Identity

We show that the cubic theta functions satisfy two distinct coupled systems of nonlinear differential equations. The resulting relations are analogous to Ramanujan's differential equations for Eisenstein series on the full modular group. We deduce the cubic analogs presented here from trigonometric series identities arising in Ramanujan's original paper on Eisenstein series. Several consequences of these differential equations are established, including a short proof of a famous cubic theta function identity derived by J. M. Borwein and P. B. Borwein.

scholarly journals On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2111
Author(s):  
Ahmed M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions ◽  
Integral Condition ◽  
Coupled System ◽  
Coupled Systems ◽  
Integral Conditions ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Condition

It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering. Here we are concerned with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

scholarly journals On a Coupled System of Random and Stochastic Differential Equations with Nonlocal Stochastic Integral Conditions

2021 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Foued
Keyword(s):  
Differential Equations ◽  
Continuous Dependence ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions ◽  
Coupled System ◽  
Coupled Systems ◽  
Integral Conditions ◽  
Uniqueness Of The Solution

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

scholarly journals A Method of Directly Defining the inverse Mapping for a HIV infection of CD4+ T-cells model

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mangalagama Dewasurendra ◽  
Ying Zhang ◽  
Noah Boyette ◽  
Ifte Islam ◽  
Kuppalapalle Vajravelu
Keyword(s):  
T Cells ◽  
Differential Equations ◽  
Hiv Infection ◽  
Cd4 T Cells ◽  
Applied Mathematics ◽  
Nonlinear Differential Equations ◽  
Cd4 T Cell ◽  
Analysis Method ◽  
Inverse Mapping ◽  
Homotopy Analysis

AbstractIn 2015, Shijun Liao introduced a new method of directly defining the inverse mapping (MDDiM) to approximate analytically a nonlinear differential equation. This method, based on the Homotopy Analysis Method (HAM) was proposed to reduce the time it takes in solving a nonlinear equation. Very recently, Dewasurendra, Baxter and Vajravelu (Applied Mathematics and Computation 339 (2018) 758–767) extended the method to a system of two nonlinear differential equations. In this paper, we extend it further to obtain the solution to a system of three nonlinear differential equations describing the HIV infection of CD4+ T-cells. In addition, we analyzed the advantages of MDDiM over HAM, in obtaining the numerical results. From these results, we noticed that the infected CD4+ T-cell density increases with the number of virions N; but decreases with the blanket death rate μI.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

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