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Journal articles on the topic 'System of nonlinear differential equations'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Kosek, Zdeněk. "Nonlinear boundary value problem for a system of nonlinear ordinary differential equations." Časopis pro pěstování matematiky 110, no. 2 (1985): 130–44. http://dx.doi.org/10.21136/cpm.1985.108595.

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2

Tchaban, Vasyl, and Taras Ryzhyi. "Algebraic-differential equations of a nonlinear pass-through quadripole." Computational Problems of Electrical Engineering 13, no. 1 (2023): 35–38. http://dx.doi.org/10.23939/jcpee2023.01.035.

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A method of forming algebraic-differential equations of a nonlinear pass-through active quadripole, which connect its independent pole currents and independent polar voltages, is proposed. The difficulty of the analysis lies in the fact that some of both internal and external unknowns may be under the symbol of differentiation. The common differential equations of the system of internal and external currents and voltages act as starting information for this formation. The method is demonstrated on two cases of the formation of corresponding algebraic-differential equations of systems as formed

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3

Shan, Li Jun, Xue Fang, and Wei Dong He. "Nonlinear Dynamic Model and Equations of RV Transmission System." Advanced Materials Research 510 (April 2012): 536–40. http://dx.doi.org/10.4028/www.scientific.net/amr.510.536.

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The nonlinear dynamics model of gearing system is developed based on RV transmission system. The influence of the nonlinear factors as time-varying meshing stiffness, backlash of the gear pairs and errors is considered. By means of the Lagrange equation the multi-degree-of-freedom differential equations of motion are derived. The differential equations are very hard to solve for which are characterized by positive semi-definition, time-variation and backlash-type nonlinearity. And linear and nonlinear restoring force are coexist in the equations. In order to solve easily, the differential equa

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4

BILYI, Leonid, Oleh POLISHCHUK, Svitlana LISEVICH, Anatoly ZALIZETSKY, and Vasiliy MELNIK. "MODELING OF NONLINEAR DYNAMIC SYSTEMS ON THE BASIS OF THE SYSTEM SENSITIVITY MODEL TO ITS INITIAL CONDITIONS." Herald of Khmelnytskyi National University. Technical sciences 309, no. 3 (2022): 99–103. http://dx.doi.org/10.31891/2307-5732-2022-309-3-99-103.

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A typical approach for building and analyzing an object model is presented. It is determined that the tasks of analysis of nonlinear systems consist of: calculation of transients and established processes; determination of static and dynamic stability of the found processes; calculation of the sensitivity of the initial characteristics of the system to changes in its internal and external parameters. It is established that the efficiency of the analysis as a whole is determined not only by the efficiency of the algorithms of each of the stages of calculation, but also by the consistency of the

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5

Pongérard, Patrice. "NONLINEAR SYSTEM OF SINGULAR PARTIAL DIFFERENTIAL EQUATIONS." Journal of Mathematical Sciences: Advances and Applications 43 (January 10, 2017): 31–53. http://dx.doi.org/10.18642/jmsaa_7100121748.

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6

Tunç, Cemil, and Osman Tunç. "On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order." Mathematics 10, no. 22 (2022): 4235. http://dx.doi.org/10.3390/math10224235.

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In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered. Qualitative properties of solutions called the global asymptotic stability, integrability and boundedness of solutions of the second-order scalar nonlinear integro-differential equation and the nonlinear system of nonlinear integro-differential equations with infinite delays are discussed. In the article, new explicit qualitative conditions are presented for solutions of both the second-order scalar nonlinear integro-di

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7

Khattri, Sanjay Kumar. "Nonlinear elliptic problems with the method of finite volumes." Differential Equations and Nonlinear Mechanics 2006 (2006): 1–16. http://dx.doi.org/10.1155/denm/2006/31797.

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We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.

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8

Kaunda, Modify A. E. "Semi-closed-form solutions of the van der Pol oscillator system." E3S Web of Conferences 505 (2024): 03015. http://dx.doi.org/10.1051/e3sconf/202450503015.

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Second order vector-valued nonlinear differential equations occurring in science and engineering have been considered which generally do not have closed-form solutions. Explicit incremental semi-analytical numerical solution procedures for nonlinear multiple-degree-of-freedom systems have been developed. Higher order equivalent differential equations were formulated and then subsequent values of vectors were updated using explicit Taylor series expansions. As the time-step tends to zero, the values of displacement and velocity are exact in the Taylor series expansions involving as many higher

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9

Leibov, Roman. "Piecewise continuous approach to nonlinear differential equations approximation problem of computational structural mechanics." MATEC Web of Conferences 251 (2018): 04024. http://dx.doi.org/10.1051/matecconf/201825104024.

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This paper presents a nonlinear differential equations system piecewise continuous approximation. The piecewise continuous approximation improves piecewise linear approximation through reducing the errors at the boundaries of different linear differential equations systems areas. The matrices of piecewise continuous differential and algebraic equations systems are estimated using nonlinear differential equations system time responses and random search method. The results of proposed approach application are presented.

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10

Yuldashev, T. K. "О нелокальной краевой задаче для интегро-дифференциального уравнения в частных производных с вырожденным ядром". Владикавказский математический журнал, № 2 (22 червня 2022): 130–41. http://dx.doi.org/10.46698/h5012-2008-4560-g.

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On a nonlocal boundary value problem for a partial integro-differential equations with degenerate kernel\Abstracteng{In this article the problems of the unique classical solvability and theconstruction of the solution of a nonlinear boundary value problem for a fifth orderpartial integro-differential equations with degenerate kernel are studied. Dirichletboundary conditions are specified with respect to the spatial variable. So, the Fourierseries method, based on the separation of variables is used. A countable system of~thesecond order ordinary integro-differential equations with degenerate k

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11

Yang, Zhichun, and Daoyi Xu. "Attractivity of nonlinear impulsive delay differential equations." Journal of Applied Mathematics and Stochastic Analysis 2006 (July 13, 2006): 1–12. http://dx.doi.org/10.1155/jamsa/2006/83152.

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The attractivity of nonlinear differential equations with time delays and impulsive effects is discussed. We obtain some criteria to determine the attracting set and attracting basin of the impulsive delay system by developing an impulsive delay differential inequality and introducing the concept of nonlinear measure. Examples and their simulations illustrate the effectiveness of the results and different asymptotical behaviors between the impulsive system and the corresponding continuous system.

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12

Saeed, Umer. "Sine–cosine wavelets operational matrix method for fractional nonlinear differential equation." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 04 (2019): 1950026. http://dx.doi.org/10.1142/s0219691319500267.

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In this paper, we present a solution method for fractional nonlinear ordinary differential equations. We propose a method by utilizing the sine–cosine wavelets (SCWs) in conjunction with quasilinearization technique. The fractional nonlinear differential equations are transformed into a system of discrete fractional differential equations by quasilinearization technique. The operational matrices of fractional order integration for SCW are derived and utilized to transform the obtained discrete system into systems of algebraic equations and the solutions of algebraic systems lead to the solutio

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13

Wang, Wenli, and Junyan Bao. "Existence Results for Nonlinear Impulsive System with Causal Operators." Mathematics 12, no. 17 (2024): 2755. http://dx.doi.org/10.3390/math12172755.

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In this paper, we establish sufficient conditions for some existence results for nonlinear impulsive differential equations involving causal operators. Our method is based on the monotone iterative technique, a new differential inequality, and the Schauder fixed point theorem. Moreover, we consider three impulsive differential equations as applications to verify our theoretical results.

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14

Kucche, Kishor D., and Juan J. Trujillo. "Theory of System of Nonlinear Fractional Differential Equations." Progress in Fractional Differentiation and Applications 3, no. 1 (2017): 7–18. http://dx.doi.org/10.18576/pfda/030102.

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15

E A A, Ziada. "Solution of Nonlinear System of Fractional Differential Equations." International Journal of Mathematics Trends and Technology 67, no. 9 (2021): 65–71. http://dx.doi.org/10.14445/22315373/ijmtt-v67i9p507.

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16

Bonfoh, A. Sanih. "On a system of nonlinear partial differential equations." Bulletin of the Australian Mathematical Society 71, no. 3 (2005): 435–46. http://dx.doi.org/10.1017/s0004972700038442.

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We consider a generalised Cahn-Hilliard system with elasticity based on constitutives laws proposed by Gurtin, with a logarithmic free energy. We obtain some results on the existence and uniqueness of solutions.

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17

Chumakov, G. A. "Dynamics of a system of nonlinear differential equations." Siberian Mathematical Journal 48, no. 5 (2007): 949–60. http://dx.doi.org/10.1007/s11202-007-0098-x.

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18

Li, Chenkuan, and Joshua Beaudin. "On the Nonlinear Integro-Differential Equations." Fractal and Fractional 5, no. 3 (2021): 82. http://dx.doi.org/10.3390/fractalfract5030082.

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The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s contractive principle, the multivariate Mittag–Leffler function and Babenko’s approach. We also provide a few examples to demonstrate the use of our main theorems by convolutions and the gamma function.

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19

Motsa, S. S., F. G. Awad, Z. G. Makukula, and P. Sibanda. "The Spectral Homotopy Analysis Method Extended to Systems of Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/241594.

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The spectral homotopy analysis method is extended to solutions of systems of nonlinear partial differential equations. The SHAM has previously been successfully used to find solutions of nonlinear ordinary differential equations. We solve the nonlinear system of partial differential equations that model the unsteady nonlinear convective flow caused by an impulsively stretching sheet. The numerical results generated using the spectral homotopy analysis method were compared with those found using the spectral quasilinearisation method (SQLM) and the two results were in good agreement.

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20

Kaptsov, O. V. "B-determining equations: applications to nonlinear partial differential equations." European Journal of Applied Mathematics 6, no. 3 (1995): 265–86. http://dx.doi.org/10.1017/s0956792500001832.

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We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.

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21

Et. al., Dr K. V. Tamil Selvi ,. "Analytical solution of Velocities and Temperature fields using Homotopy Analysis Method." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 1S (2021): 691–700. http://dx.doi.org/10.17762/turcomat.v12i1s.1975.

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In this paper, analysis of nonlinear partial differential equations on velocities and temperature with convective boundary conditions are investigated. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. The system of nonlinear differential equations are solved using Homotopy Analysis Method (HAM). An analytical solution is obtained for the values of Magnetic parameter M2, Prandtl number Pr, Porosity parameter

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22

Shanan, Ibrahim A., and Mudhir A. Abdul Hussain. "Bifurcation Solutions of a System of Nonlinear Differential Equations." Journal of Kufa for Mathematics and Computer 2, no. 3 (2015): 61–67. http://dx.doi.org/10.31642/jokmc/2018/020306.

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This paper study the bifurcation solutions of a System of nonlinear differential equations, by using local method of Lyapunov â€“Schmidt . The reduced equation has been found as a system of nonlinear algebraic equations . We gave a Geometric description of The Discriminate set with the spreading of the regular solutions of a specified system.

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23

Tchaban, Vasyl. "Differential equations of a nonlinear multipolar element." Computational Problems of Electrical Engineering 12, no. 1 (2022): 45–48. http://dx.doi.org/10.23939/jcpee2022.01.045.

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A method for forming nonlinear differential equations of a multipololar element, which connect its independent pole currents and independent polar voltages, is proposed. The difficulty of the analysis is that some of the internal and external unknowns may be under the symbol of differentiation. The starting information for this formation is the common differential equations of the system of internal and external currents and voltages. The method is demonstrated on the case of formation of the corresponding differential equations of the system as such that is formed by bipolar elements. The a

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24

Hassan, Habibu, and Alhaji Tahir. "Solution of System of First Order Nonlinear Non-Homogeneous Fuzzy Ordinary Differential Equations by Embedding Method." UMYU Scientifica 2, no. 3 (2023): 60–64. http://dx.doi.org/10.56919/usci.2323.010.

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In this study, a system of first order nonlinear non-homogeneous fuzzy ordinary differential equations will be examine in fuzzy environment and solved using embedding method. The results of nonlinear non-homogeneous fuzzy ordinary differential equations are established which followed the form of SxS matrices and all the components of the matrices are real functions of time denoted by t. The accuracy of the results obtained is tested on some constructed example and recommended that further study should consider odd and even system of nonlinear non-homogeneous fuzzy ordinary differential equatio

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25

Verma, Anjali, and Ram Jiwari. "Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 7 (2015): 1574–89. http://dx.doi.org/10.1108/hff-08-2014-0240.

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Purpose – The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM). Design/methodology/approach – The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings – The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that th

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26

Deswita, Leli. "Pemodelan Matematika Perpindahan Panas Konveksi Campuran (Mixed Convection) pada Pelat Horizontal." Jurnal Matematika "MANTIK" 3, no. 2 (2017): 96–100. http://dx.doi.org/10.15642/mantik.2017.3.2.96-100.

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This study examines and analyzes mathematical model of mixed convection in horizontal plate. The heat transfer uses the model of a two dimensional nonlinear partial differential equations system. Then, this equation is derived first into the dimensionless equation form, and then it is changed into system of nonlinear ordinary differential equations form using similarity transformation. This system of nonlinear ordinary differential equations is solved by using the finite-difference scheme method, also with the mathematics program with software Matlab. The results obtained form this program is

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27

Gepreel, Khaled A., Taher A. Nofal, and Fawziah M. Alotaibi. "Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/756896.

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We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear di

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28

Kovalchuk, Olya, Myhaylo Bartish, and Natalya Ogorodnyk. "On some iterative method for solving nonlinear equations." Modeling, Control and Information Technologies, no. 3 (November 5, 2019): 7–8. http://dx.doi.org/10.31713/mcit.2019.28.

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We study an iterative differential-difference three-step method for solving system of nonlinear equations, which uses, instead of the Jacobian, the sum of derivate of differentiable parts of operator and divided difference of nondifferentiable parts. The numerical examples illustrate how the methods works.

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29

ABDUVAHOBOV, T. A. "SYSTEM OF IMPULSIVE DIFFERENTIAL EQUATIONS WITH A PRODUCTOF TWO NONLINEAR FUNCTIONS AND NONLINEAR BOUNDARY CONDITIONS." Челябинский физико-математический журнал 9, no. 4 (2024): 539–51. https://doi.org/10.47475/2500-0101-2024-9-4-539-551.

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A nonlocal two-point boundary value problem for pulse systems of ordinary differential equations of the first order with nonlinear conditions, including derivatives of an unknown vector function, is investigated. The system of differential equations contains the product of two nonlinear vector functions, for each of which the Lipschitz condition is satisfied. The existence, uniqueness and continuous dependence of the solution on the given functions are proved. The problem is reduced to a system of nonlinear functional integral equations in a Banach space. The method of successive approximation

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30

Pinto, Manuel. "Nonlinear delay-differential equations with small lag." International Journal of Mathematics and Mathematical Sciences 20, no. 1 (1997): 137–46. http://dx.doi.org/10.1155/s0161171297000203.

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31

Nasir, Fuad. "Use of Reversion Method to Solve Mathematical Models on Series Electrical Circuits (Rl) with Nonlinear Inductors." Jurnal Improsci 1, no. 3 (2023): 126–32. http://dx.doi.org/10.62885/improsci.v1i3.147.

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Forming a mathematical model of a series electrical circuit with a nonlinear inductor obtained based on Kirchoff's laws one and two takes the form of a nonlinear differential equation. Approach methods are used to determine the electric current in the circuit, including the Reversion Method, namely by converting nonlinear differential equations into a system of linear differential equations.

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32

Moosavi Noori, Seyyedeh Roodabeh, and Nasir Taghizadeh. "Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations." International Journal of Differential Equations 2021 (April 29, 2021): 1–16. http://dx.doi.org/10.1155/2021/6696414.

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In this work, we study the sufficient condition for convergence of the reduced differential transform method for nonlinear differential equations. The main power of this method is its ability and flexibility in solving linear and nonlinear problems properly and easily and obtain solutions both numerically and analytically. Simple approaches of reduced differential transform method and the convergence results for different classes of differential equations such as linear and nonlinear ordinary, partial, fractional, and system of differential equations are briefly discussed. Eight examples are c

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33

Taieb, Amele, and Zoubir Dahmani. "A coupled system of nonlinear differential equations involving m nonlinear terms." Georgian Mathematical Journal 23, no. 3 (2016): 447–58. http://dx.doi.org/10.1515/gmj-2016-0014.

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AbstractIn this paper, we study a coupled system of nonlinear fractional differential equations involving m nonlinear terms, ${m\in\mathbb{N^{*}}}$. We begin by introducing a new Banach space. Then, we establish new existence and uniqueness results using the Banach contraction principle. We also prove an existence result using the Schaefer fixed point theorem. Finally, we give some illustrative examples.

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34

FILIPPOVA, TATIANA. "SET-VALUED DYNAMICS IN PROBLEMS OF MATHEMATICAL THEORY OF CONTROL PROCESSES." International Journal of Modern Physics B 26, no. 25 (2012): 1246010. http://dx.doi.org/10.1142/s0217979212460101.

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The dynamics and properties of set-valued states of differential control systems with uncertainties in initial data are studied. It is assumed that the dynamical system has a special structure, in which nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates. We construct external and internal ellipsoidal estimates of reachable sets of nonlinear control system and find differential equations of proposed ellipsoidal estimates of reachable sets of nonlinear control system. The results obtained for quadratic system nonlinearities are extended t

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35

Murty, K. N., and Michael D. Shaw. "Stability analysis of nonlinear Lyapunov systems associated with an nth order system of matrix differential equations." Journal of Applied Mathematics and Stochastic Analysis 15, no. 2 (2002): 141–50. http://dx.doi.org/10.1155/s104895330200014x.

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This paper introduces the notion of Lipschitz stability for nonlinear nth order matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear nth order matrix Lyapunov differential system. We study observability and controllability of a special system of nth order nonlinear Lyapunov systems.

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36

Ying, Zu-Guang, and Yi-Qing Ni. "A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters." Journal of Vibration and Control 26, no. 13-14 (2019): 1260–72. http://dx.doi.org/10.1177/1077546319892429.

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A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equat

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37

Mardanov, M. J., Y. A. Sharifov, and K. E. Ismayilova. "Existence and uniqueness of solutions for the system ofintegro-differential equations with three-point and nonlinear integral boundary conditions." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 99, no. 3 (2020): 23–37. http://dx.doi.org/10.31489/2020m3/26-37.

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The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Scha

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38

Redkina, Zakinyan, Zakinyan, Surneva, and Yanovskaya. "Bäcklund Transformations for Nonlinear Differential Equations and Systems." Axioms 8, no. 2 (2019): 45. http://dx.doi.org/10.3390/axioms8020045.

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In this work, new Bäcklund transformations (BTs) for generalized Liouville equations were obtained. Special cases of Liouville equations with exponential nonlinearity that have a multiplier that depends on the independent variables and first-order derivatives from the function were considered. Two- and three-dimensional cases were considered. The BTs construction is based on the method proposed by Clairin. The solutions of the considered equations have been found using the BTs, with a unified algorithm. In addition, the work develops the Clairin’s method for the system of two third-order equat

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39

Tovboyev, A. N., D. Sh Mardonov, A. X. Mamatazimov, and S. S. Samatova. "Analysis of subharmonic oscillations in multi-phase ferroresonance circuits using a mathematical model." Journal of Physics: Conference Series 2094, no. 5 (2021): 052048. http://dx.doi.org/10.1088/1742-6596/2094/5/052048.

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Abstract The article about solution of system of nonlinear differential equations that are almost impossible to solve by analytical methods by constructing a mathematical model of nonlinear oscillations occurring in three-phase ferroresonance circuits. A system of nonlinear differential equations was formed by approximating the volt-ampere characteristics of a ferromagnetic element in a ferroresonance circuit. Mathematical models for solving technical problems characterizing subharmonic oscillation processes in three-phase ferroresonance circuits and systems using the finite-difference method

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40

Boykov, Ilya, Vladimir Roudnev, and Alla Boykova. "Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks." Mathematics 10, no. 13 (2022): 2207. http://dx.doi.org/10.3390/math10132207.

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A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficie

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41

Ali, Musrrat, Hemant Gandhi, Amit Tomar, and Dimple Singh. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws." Mathematics 11, no. 11 (2023): 2465. http://dx.doi.org/10.3390/math11112465.

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The analysis of differential equations using Lie symmetry has been proved a very robust tool. It is also a powerful technique for reducing the order and nonlinearity of differential equations. Lie symmetry of a differential equation allows a dynamic framework for the establishment of invariant solutions of initial value and boundary value problems, and for the deduction of laws of conservations. This article is aimed at applying Lie symmetry to the fractional-order coupled nonlinear complex Hirota system of partial differential equations. This system is reduced to nonlinear fractional ordinary

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42

Adomian, G. "Systems of nonlinear partial differential equations." Journal of Mathematical Analysis and Applications 115, no. 1 (1986): 235–38. http://dx.doi.org/10.1016/0022-247x(86)90038-7.

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43

Fife, Paul C. "Systems of nonlinear partial differential equations." Mathematical Biosciences 79, no. 1 (1986): 119–20. http://dx.doi.org/10.1016/0025-5564(86)90022-2.

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44

Singh, Inderdeep. "Wavelet based method for solving generalized Burger’s type equations." International Journal of Computational Materials Science and Engineering 08, no. 04 (2019): 1950020. http://dx.doi.org/10.1142/s2047684119500209.

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In this work, an efficient numerical method is proposed for solving generalized Burger’s type equations. The generalized Burger’s type equations are first converted into a nonlinear ordinary differential equation by choosing some suitable wave variable transformation. Linearize such nonlinear differential equations by using quasilinearization technique. For solving algebraic system of linear equations Haar wavelet-based collocation method is used. A distinct feature of the proposed method is their simple applicability in a variety of two- and three- dimensional nonlinear partial differential e

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45

Zhang, Jingyuan. "5D Nonlinear Dynamic Evolutionary System in Real Estate Market." Complexity 2021 (January 11, 2021): 1–15. http://dx.doi.org/10.1155/2021/6670222.

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In this paper, we propose a new predator-prey nonlinear dynamic evolutionary model of real estate enterprises considering the large, medium, and small real estate enterprises for three different prey teams. A 5D predator-prey nonlinear dynamic evolutionary system in the real estate market is established, where the large, medium, and small real estate enterprises correspond to three differential equations, provincial and local officials, and the central government correspond to the other two differential equations. Nonlinear dynamic analysis on a 5D predator-prey evolutionary system in the real

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46

Anac, Halil. "A Local Fractional Elzaki Transform Decomposition Method for the Nonlinear System of Local Fractional Partial Differential Equations." Fractal and Fractional 6, no. 3 (2022): 167. http://dx.doi.org/10.3390/fractalfract6030167.

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In this paper, the nonlinear system of local fractional partial differential equations is solved via local fractional Elzaki transform decomposition method. The local fractional Elzaki decomposition transform method combines a local fractional Elzaki transform and the Adomian decomposition method. Applications related to the nonlinear system of local fractional partial differential equations are presented.

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47

Eshbekov and Mannonov. "INTEGRATION OF A NONLINEAR HIROTA TYPE EQUATION WITH ADDITIONAL TERMS." UZBEK MATHEMATICAL JOURNAL 68, no. 1 (2024): 46–56. http://dx.doi.org/10.29229/uzmj.2024-1-7.

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In this paper, the inverse spectral problem method is used to integrate a nonlinear Hirota-type equation with additional terms in the class of periodic functions. The evolution of the spectral data of the periodic Dirac operator is introduced, the coefficient of Dirac operator is a solution to the nonlinear Hirota type equation with additional terms. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of six times continuously differentiable periodic infinite-zone functions is proved.

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48

Assanova, A. T., S. S. Zhumatov, S. T. Mynbayeva, and S. G. Karakenova. "On solvability of boundary value problem for a nonlinear Fredholm integro-differential equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 105, no. 1 (2022): 25–34. http://dx.doi.org/10.31489/2022m1/25-34.

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The paper proposes a constructive method to solve a nonlinear boundary value problem for a Fredholm integro-differential equation. Using D.S. Dzhumabaev parametrization method, the problem under consideration is transformed into an equivalent boundary value problem for a system of nonlinear integrodifferential equations with parameters on the subintervals. When applying the parametrization method to a nonlinear Fredholm integro-differential equation, the intermediate problem is a special Cauchy problem for a system of nonlinear integro-differential equations with parameters. By substitution th

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Bluman, G. W., and S. Kumei. "Symmetry-based algorithms to relate partial differential equations: I. Local symmetries." European Journal of Applied Mathematics 1, no. 3 (1990): 189–216. http://dx.doi.org/10.1017/s0956792500000176.

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Simple and systematic algorithms for relating differential equations are given. They are based on comparing the local symmetries admitted by the equations. Comparisons of the infinitesimal generators and their Lie algebras of given and target equations lead to necessary conditions for the existence of mappings which relate them. Necessary and sufficient conditions are presented for the existence of invertible mappings from a given nonlinear system of partial differential equations to some linear system of equations with examples including the hodograph and Legendre transformations, and the lin

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Shaikhet, Leonid. "Stability of the Exponential Type System of Stochastic Difference Equations." Mathematics 11, no. 18 (2023): 3975. http://dx.doi.org/10.3390/math11183975.

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The method of studying the stability in the probability for nonlinear systems of stochastic difference equations is demonstrated on two systems with exponential and fractional nonlinearities. The proposed method can be applied to nonlinear systems of higher dimensions and with other types of nonlinearity, both for difference equations and for differential equations with delay.

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