Relevant bibliographies by topics / Integro-differential equations. Nonlinear integral equations

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Integro-differential equations. Nonlinear integral equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Integro-differential equations. Nonlinear integral equations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Integro-differential equations. Nonlinear integral equations"

1

GIL', M. I. "POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS." Analysis and Applications 07, no. 04 (2009): 405–18. http://dx.doi.org/10.1142/s0219530509001475.

Full text
Abstract:
We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.
APA, Harvard, Vancouver, ISO, and other styles
2

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.

Full text
Abstract:
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 Schaefer’s theorem.
APA, Harvard, Vancouver, ISO, and other styles
3

Mousa, Mohamed M., and Fahad Alsharari. "Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations." Mathematics 9, no. 18 (2021): 2244. http://dx.doi.org/10.3390/math9182244.

Full text
Abstract:
In this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations.
APA, Harvard, Vancouver, ISO, and other styles
4

Hemeda, A. A. "A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations." International Journal of Computational Methods 15, no. 03 (2018): 1850016. http://dx.doi.org/10.1142/s0219876218500160.

Full text
Abstract:
In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.
APA, Harvard, Vancouver, ISO, and other styles
5

Its, A. R., A. G. Izergin, V. E. Korepin, and N. A. Slavnov. "DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS." International Journal of Modern Physics B 04, no. 05 (1990): 1003–37. http://dx.doi.org/10.1142/s0217979290000504.

Full text
Abstract:
The quantum nonlinear Schrödinger equation (one dimensional Bose gas) is considered. Classification of representations of Yangians with highest weight vector permits us to represent correlation function as a determinant of a Fredholm integral operator. This integral operator can be treated as the Gelfand-Levitan operator for some new differential equation. These differential equations are written down in the paper. They generalize the fifth Painlève transcendent, which describe equal time, zero temperature correlation function of an impenetrable Bose gas. These differential equations drive the quantum correlation functions of the Bose gas. The Riemann problem, associated with these differential equations permits us to calculate asymp-totics of quantum correlation functions. Quantum correlation function (Fredholm determinant) plays the role of τ functions of these new differential equations. For the impenetrable Bose gas space and time dependent correlation function is equal to τ function of the nonlinear Schrödinger equation itself, For a penetrable Bose gas (finite coupling constant c) the correlator is τ-function of an integro-differentiation equation.
APA, Harvard, Vancouver, ISO, and other styles
6

Castro, L. P., and A. M. Simões. "Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations." Filomat 31, no. 17 (2017): 5379–90. http://dx.doi.org/10.2298/fil1717379c.

Full text
Abstract:
We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of semi-Hyers-Ulam-Rassias stability, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.
APA, Harvard, Vancouver, ISO, and other styles
7

Iskandarova, Gulistan, and Dogan Kaya. "Symmetry solution on fractional equation." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7, no. 3 (2017): 255–59. http://dx.doi.org/10.11121/ijocta.01.2017.00498.

Full text
Abstract:
As we know nearly all physical, chemical, and biological processes in nature can be described or modeled by dint of a differential equation or a system of differential equations, an integral equation or an integro-differential equation. The differential equations can be ordinary or partial, linear or nonlinear. So, we concentrate our attention in problem that can be presented in terms of a differential equation with fractional derivative. Our research in this work is to use symmetry transformation method and its analysis to search exact solutions to nonlinear fractional partial differential equations.
APA, Harvard, Vancouver, ISO, and other styles
8

Tate, Shivaji, V. V. Kharat, and H. T. Dinde. "On nonlinear mixed fractional integro-differential equations with positive constant coefficient." Filomat 33, no. 17 (2019): 5623–38. http://dx.doi.org/10.2298/fil1917623t.

Full text
Abstract:
In this paper, we study the existence and other properties of the solution of nonlinear mixed fractional integro-differential equations with constant coefficient. Also with the help of integral inequality of mixed type, we prove the continuous dependence of the solutions on the initial conditions.
APA, Harvard, Vancouver, ISO, and other styles
9

Polyanin, A. D., and A. I. Zhurov. "Exact solutions to some classes of nonlinear integral, integro-functional, and integro-differential equations." Doklady Mathematics 77, no. 2 (2008): 315–19. http://dx.doi.org/10.1134/s1064562408020403.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Bainov, Drumi D., and Snezhana G. Hristova. "Integral inequalities of Gronwall type for piecewise continuous functions." Journal of Applied Mathematics and Stochastic Analysis 10, no. 1 (1997): 89–94. http://dx.doi.org/10.1155/s1048953397000099.

Full text
Abstract:
In this paper we generalize the integral inequality of Gronwall and study the continuous dependence of the solution of the initial value problem for nonlinear impulsive integro-differential equations of Volterra type on the initial conditions.
APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic "Integro-differential equations. Nonlinear integral equations"

1

Geigant, Edith. "Nichtlineare Integro-Differential-Gleichungen zur Modellierung interaktiver Musterbildungsprozesse auf S¹." Bonn : Rheinische Friedrich-Wilhelms-Universität, 1999. http://catalog.hathitrust.org/api/volumes/oclc/45517690.html.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Jin, Chao. "Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3256468.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Davidsen, Stein-Olav Hagen. "Nonlinear integro-differential Equations : Numerical Solutions by using Spectral Methods." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22682.

Full text
Abstract:
This article deals with numerical solutions of nonlinear integro-differential convection-diffusion equations using spectral methods. More specifically, the spectral vanishing viscosity method is introduced and analyzed to show that its family of numerical solutions is compact, and that its solutions converge to the vanishing viscosity solutions. The method is implemented in code, and numerical results including qualitative plots and convergence estimates are given. The article concludes with a discussion of some important implementation concerns and recommendations for further work related to the topic.
APA, Harvard, Vancouver, ISO, and other styles
4

Hadad, Yaron. "Integrable Nonlinear Relativistic Equations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293490.

Full text
Abstract:
This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 Einstein equation the Belinski-Zakharov transformation is explored. It is used to derive explicit formula for N gravitational solitons on arbitrary diagonal background. In particular, the method is used to derive gravitational solitons on the Einstein-Rosen background. The similarities and differences between the attributes of the solitons of the symmetric Chiral field equation and those of the 1+1 Einstein equation are emphasized, and their origin is pointed out. For the 1+2 Einstein equation, new equations describing diagonal metrics are derived and their compatibility is proven. Different gravitational waves are studied that naturally extend the class of Bondi-Pirani-Robinson waves. It is further shown that the Bondi-Pirani-Robinson waves are stable with respect to perturbations of the spacetime. Their stability is closely related to the stability of the Schwarzschild black hole and the relation between the two allows to conjecture about the stability of a wide range of gravitational phenomena. Lastly, a new set of equations that describe weak gravitational waves is derived. This new system of equations is closely and fundamentally connected with the nonlinear Schrödinger equation and can be properly called the nonlinear Schrödinger-Einstein equations. A few preliminary solutions are constructed.
APA, Harvard, Vancouver, ISO, and other styles
5

Dimakos, Michail. "Linear, linearisable and integrable nonlinear PDEs." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607875.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Jakubowski, Volker G. "Nonlinear elliptic parabolic integro differential equations with L-data existence, uniqueness, asymptotic /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=966250141.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Hao, Han. "Traveling Wave Solutions of Integro-differential Equations of One-dimensional Neuronal Networks." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24244.

Full text
Abstract:
Traveling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) traveling wave solutions are established. Some faults in previous studies are corrected.
APA, Harvard, Vancouver, ISO, and other styles
8

Scoufis, George. "An Application of the Inverse Scattering Transform to some Nonlinear Singular Integro-Differential Equations." University of Sydney, Mathematics and Statistics, 1999. http://hdl.handle.net/2123/412.

Full text
Abstract:
ABSTRACT The quest to model wave propagation in various physical systems has produced a large set of diverse nonlinear equations. Nonlinear singular integro-differential equations rank amongst the intricate nonlinear wave equations available to study the classical problem of wave propagation in physical systems. Integro-differential equations are characterized by the simultaneous presence of integration and differentiation in a single equation. Substantial interest exists in nonlinear wave equations that are amenable to the Inverse Scattering Transform (IST). The IST is an adroit mathematical technique that delivers analytical solutions of a certain type of nonlinear equation: soliton equation. Initial value problems of numerous physically significant nonlinear equations have now been solved through elegant and novel implementations of the IST. The prototype nonlinear singular integro-differential equation receptive to the IST is the Intermediate Long Wave (ILW) equation, which models one-dimensional weakly nonlinear internal wave propagation in a density stratified fluid of finite total depth. In the deep water limit the ILW equation bifurcates into a physically significant nonlinear singular integro-differential equation known as the 'Benjamin-Ono' (BO) equation; the shallow water limit of the ILW equation is the famous Korteweg-de Vries (KdV) equation. Both the KdV and BO equations have been solved by dissimilar implementations of the IST. The Modified Korteweg-de Vries (MKdV) equation is a nonlinear partial differential equation, which was significant in the historical development of the IST. Solutions of the MKdV equation are mapped by an explicit nonlinear transformation known as the 'Miura transformation' into solutions of the KdV equation. Historically, the Miura transformation manifested the intimate connection between solutions of the KdV equation and the inverse problem for the one-dimensional time independent Schroedinger equation. In light of the MKdV equation's significance, it is natural to seek 'modified' versions of the ILW and BO equations. Solutions of each modified nonlinear singular integro-differential equation should be mapped by an analogue of the original Miura transformation into solutions of the 'unmodified' equation. In parallel with the limiting cases of the ILW equation, the modified version of the ILW equation should reduce to the MKdV equation in the shallow water limit and to the modified version of the BO equation in the deep water limit. The Modified Intermediate Long Wave (MILW) and Modified Benjamin-Ono (MBO) equations are the two nonlinear singular integro-differential equations that display all the required attributes. Several researchers have shown that the MILW and MBO equations exhibit the signature characteristic of soliton equations. Despite the significance of the MILW and MBO equations to soliton theory, and the possible physical applications of the MILW and MBO equations, the initial value problems for these equations have not been solved. In this thesis we use the IST to solve the initial value problems for the MILW and MBO equations on the real-line. The only restrictions that we place on the initial values for the MILW and MBO equations are that they be real-valued, sufficiently smooth and decay to zero as the absolute value of the spatial variable approaches large values.
APA, Harvard, Vancouver, ISO, and other styles
9

Kim, Tae Eun. "Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Grupcev, Vladimir. "Symbolic computations of exact solutions to nonlinear integrable differential equations." [Tampa, Fla.] : University of South Florida, 2007. http://purl.fcla.edu/usf/dc/et/SFE0002025.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Integro-differential equations. Nonlinear integral equations"

1

O'Regan, Donal. Existence theory for nonlinear integral and integrodifferential equations. Kluwer Academic Press, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Precup, Radu. Methods in nonlinear integral equations. Kluwer Academic Publishers, 2002.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Precup, Radu. Methods in nonlinear integral equations. Kluwer Academic Publishers, 2002.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Precup, Radu. Methods in nonlinear integral equations. Springer, 2002.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Methods in nonlinear integral equations. Kluwer Academic Publishers, 2002.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Foltyńska, Izabela. Oscillatory solutions to systems of nonlinear integrodifferential equations with deviating arguments. Wydawn. Politechniki Poznańskiej, 1993.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Hallett, Andrew Hughes. Hybrid algorithms with automatic switching for solving nonlinear equation systems. Dept. of Economics, Fraser of Allander Institute, University of Strathclyde, 1996.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Wędrychowicz, Stanisław. Compactness conditions for nonlinear stochastic differential and integral equations. Wydawn. Uniwersytetu Jagiellońskiego, 2001.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Ha, Ki Sik. Nonlinear Functional Evolutions in Banach Spaces. Springer Netherlands, 2003.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Topics in nonlinear functional analysis. Courant Institute, 2001.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Integro-differential equations. Nonlinear integral equations"

1

Wazwaz, Abdul-Majid. "Volterra Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Wazwaz, Abdul-Majid. "Fredholm Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Wazwaz, Abdul-Majid. "Nonlinear Volterra Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_14.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Wazwaz, Abdul-Majid. "Nonlinear Fredholm Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Wazwaz, Abdul-Majid. "Volterra-Fredholm Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Guo, Dajun, V. Lakshmikantham, and Xinzhi Liu. "Nonlinear Integro-Differential Equations in Banach Spaces." In Nonlinear Integral Equations in Abstract Spaces. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1281-9_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Azevedo, Juarez S., Saulo P. Oliveira, Suzete M. Afonso, and Mariana P. G. da Silva. "Analysis and Spectral Element Solution of Nonlinear Integral Equations of Hammerstein Type." In Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Degasperis, A., D. Lebedev, M. Olshanetsky, S. Pakuliak, A. Perelomov, and P. Santini. "Recent Development for Integrable Integro-Differential Equations." In Nonlinear Evolution Equations and Dynamical Systems. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76172-0_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Dudley, R. M., and R. Norvaiša. "Nonlinear Differential and Integral Equations." In Springer Monographs in Mathematics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6950-7_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Pflüger, Klaus. "On Indefinite Nonlinear Neumann Problems." In Partial Differential and Integral Equations. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3276-3_25.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Integro-differential equations. Nonlinear integral equations"

1

Gururaja Rao, Lakshmi, and James T. Allison. "Generalized Viscoelastic Material Design With Integro-Differential Equations and Direct Optimal Control." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46768.

Full text
Abstract:
Rheological material properties are examples of function-valued quantities that depend on frequency (linear viscoelasticity), input amplitude (nonlinear material behavior), or both. This dependence complicates the process of utilizing these systems in engineering design. In this article, we present a methodology to model and optimize design targets for such rheological material functions. We show that for linear viscoelastic systems simple engineering design assumptions can be relaxed from a conventional spring-dashpot model to a more general linear viscoelastic relaxation kernel, K(t). While this approach expands the design space and connects system-level performance with optimal material design functions, it entails significant numerical difficulties. Namely, the associated governing equations involve a convolution integral, thus forming a system of integro-differential equations. This complication has two important consequences: 1) the equations representing the dynamic system cannot be written in a standard state space form as the time derivative function depends on the entire past state history, and 2) the dependence on prior time-history increases time derivative function computational expense. Previous studies simplified this process by incorporating parameterizations of K(t) using viscoelastic models such as Maxwell or critical gel models. While these simplifications support efficient solution, they limit the type of viscoelastic materials that can be designed. This article introduces a more general approach that can explore arbitrary K(t) designs using direct optimal control methods. In this study, we analyze a nested direct optimal control approach to optimize linear viscoelastic systems with no restrictions on K(t). The study provides new insights into efficient optimization of systems modeled using integro-differential equations. The case study is based on a passive vibration isolator design problem. The resulting optimal K(t) functions can be viewed as early-stage design targets that are material agnostic and allow for creative material design solutions. These targets may be used for either material-specific selection or as targets for later-stage design of novel materials.
APA, Harvard, Vancouver, ISO, and other styles
2

Huang, Qinghua, and Wei-Chau Xie. "Stability of SDOF Nonlinear Viscoelastic System Under the Excitation of Wide-Band Noise." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42071.

Full text
Abstract:
The stochastic stability of a single degree-of-freedom (SDOF) nonlinear viscoelastic system under the excitation of wide-band noise is studied in this paper. An example of such a system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The equation of motion is an integro-differential equation with parametric excitation. The stochastic averaging method and averaging method for integro-differential equations are applied to reduce the system. The largest Lyapunov exponents and stochastic bifurcation are studied after the averaged sytem is obtained.
APA, Harvard, Vancouver, ISO, and other styles
3

Rezounenko, Alexander. "Stability of positive solutions of local partial differential equations with a nonlinear integral delay term." In The 8'th Colloquium on the Qualitative Theory of Differential Equations. Bolyai Institute, SZTE, 2007. http://dx.doi.org/10.14232/ejqtde.2007.7.17.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Hajivand, A., and S. H. Mousavizadegan. "The Effect of Memory in Observer Design for a DP System." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38040.

Full text
Abstract:
The behavior of marine structures is investigated in regular waves using various models in frequency and time domains. In normal practice, the differential form of motion equations are used with constant hydrodynamic coefficients. Those coefficients which are added masses and damping coefficients are frequency dependent due to the memory effect. The memory effect is usually represented by a convolution integral and hence it converts the motion equations into integro-differential forms. The presence of the convolution integral makes the equations complex. However, it is necessary to take into account the memory effect in ship motion control and specially in dynamic positioning system to enhance the accuracy and obtained a more precise controller. The motion equations are solved for a DP system with memory effect and compare with the conventional model. The computations show that memory effect is important as the wave frequency increases. A nonlinear observer has been design to solve the wave filtering and state estimation problems with the memory effect. The performance of the nonlinear observer is demonstrated by computer simulations.
APA, Harvard, Vancouver, ISO, and other styles
5

Arafat, Haider N., Ali H. Nayfeh, and Char-Ming Chin. "Nonlinear Nonplanar Dynamics of Parametrically Excited Cantilever Beams." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4028.

Full text
Abstract:
Abstract The nonlinear nonplanar response of cantilever inextensional metallic beams to a principal parametric excitation of two of its “exural modes, one in each plane, is investigated. The lowest torsional frequencies of the beams considered are much larger than the frequencies of the excited modes so that the torsional inertia can be neglected. Using this condition as well as the inextensionality condition, we develop a Lagrangian whose variation leads to the two integro-partial-differential equations of Crespo da Silva and Glynn. The method of time-averaged Lagrangian is used to derive four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two interacting modes. The modulation equations exhibit the symmetry property found by Feng and Leal by analytically manipulating the interaction coefficients in the modulation equations obtained by Nayfeh and Pai by applying the method of multiple scales to the governing integro-partial-differential equations. A pseudo arclength scheme is used to trace the branches of the equilibrium solutions and an investigation of the eigenvalues of the Jacobian matrix is used to assess their stability. The equilibrium solutions experience pitchfork, saddle-node, and Hopf bifurcations. A detailed bifurcation of the dynamic solutions of the modulation equations is presented. Five branches of dynamic (periodic and chaotic) solutions were found. Two of these branches emerge from two Hopf bifurcations and the other three are isolated. The limit cycles undergo symmetry-breaking, cyclic-fold, and period-doubling bifurcations, whereas the chaotic attractors undergo attractor-merging and boundary crises.
APA, Harvard, Vancouver, ISO, and other styles
6

Messina, Eleonora. "Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0826.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Luca, Rodica, and Johnny Henderson. "Existence of positive solutions for a system of nonlinear second-order integral boundary value problems." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0596.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Huang, J. L., and W. D. Zhu. "Nonlinear Dynamics of High-Dimensional Models of a Rotating Euler-Bernoulli Beam Under the Gravity Load." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37157.

Full text
Abstract:
Nonlinear dynamic responses of an Euler-Bernoulli beam attached to a rotating rigid hub with a constant angular velocity under the gravity load are investigated. The slope angle of the centroid line of the beam is used to describe its motion, and the nonlinear integro-partial differential equation that governs the motion of the rotating hub-beam system is derived using Hamilton’s principle. Spatially discretized governing equations are derived using Lagrange’s equations based on discretized expressions of kinetic and potential energies of the system, yielding a set of second-order nonlinear ordinary differential equations with combined parametric and forced harmonic excitations due to the gravity load. The incremental harmonic balance (IHB) method is used to solve for periodic responses of high-dimensional models of the system and period-doubling bifurcation. The multivariable Floquet theory along with the precise Hsu’s method is used to investigate the stability of the periodic responses. Phase portraits and bifurcation points obtained from the IHB method agree very well with those from numerical integration.
APA, Harvard, Vancouver, ISO, and other styles
9

Obodan, Y. "Forced Vibrations of an Elastic Plate Interacting With a Layer of Granular Material." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0049.

Full text
Abstract:
Abstract A variable-structure system, consisting of a thin horizontal elastic plate, loaded by a heavy layer of granular material is considered. The system is excited by prescribed vertical vibrations of the plate boundaries. An essentially nonlinear vibrational rheological model with unilateral constraints is proposed for simulation of the layer behavior. During the coupled motion stages the layer dynamic response on the interface between plate and granular layer is described by the Volterra integro-operator relationship with nonlinear isochronic force-displacement characteristic. The governing set of equations includes the plate dynamics differential equation, an integro-differential equation of the layer dynamics, and also appropriate boundary and initial conditions. Due to utilization of the Galerkin method and Kroosh approximation, the initial set is reduced to the set of nonlinear differential equations. The latter is integrated numerically. Model identification is carried out by the computer processing of the experimental bending strain histories. Influence of the excitation parameters, height of the layer, and damping on the bending strains is analyzed. Adequate simulation of the layer behavior for one-period modes is achieved with regard to the motion periodicity, the values of the strain peaks, the critical time points and the duration of the main time stages. Analysis of numerical phase trajectories and Poincaré sections predicts transition to stochastic vibration modes and the existence of stable two-period limit cycles, when the maximum forcing acceleration is increased above 3g.
APA, Harvard, Vancouver, ISO, and other styles
10

Li, Yunhong. "Solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions." In 2015 International Conference on Automation, Mechanical Control and Computational Engineering. Atlantis Press, 2015. http://dx.doi.org/10.2991/amcce-15.2015.289.

Full text
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography