Mostrando recursos 1 - 20 de 51

  1. Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: $(m+1)$ th-Step Block Method

    Adeyeye, Oluwaseun; Omar, Zurni
    Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A $(m+\mathrm{1})\mathrm{t}\mathrm{h}$ -step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where $m$ is the order of the differential equation under consideration. The schemes obtained were...

  2. Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

    Suebcharoen, T.
    This paper studies the behavior of a predator-prey model with switching and stage-structure for predator. Bounded positive solution, equilibria, and stabilities are determined for the system of delay differential equation. By choosing the delay as a bifurcation parameter, it is shown that the positive equilibrium can be destabilized through a Hopf bifurcation. Some numerical simulations are also given to illustrate our results.

  3. Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

    Suebcharoen, T.
    This paper studies the behavior of a predator-prey model with switching and stage-structure for predator. Bounded positive solution, equilibria, and stabilities are determined for the system of delay differential equation. By choosing the delay as a bifurcation parameter, it is shown that the positive equilibrium can be destabilized through a Hopf bifurcation. Some numerical simulations are also given to illustrate our results.

  4. Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

    Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
    We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

  5. Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

    Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
    We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

  6. Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

    Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura
    We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

  7. Cyclic Growth and Global Stability of Economic Dynamics of Kaldor Type in Two Dimensions

    Nindjin, Aka Fulgence; N’Guessan, Albin Tetchi; Okou, Hypolithe; Tia, Kessé Thiban
    This article proposes nonlinear economic dynamics continuous in two dimensions of Kaldor type, the saving rate and the investment rate, which are functions of ecological origin verifying the nonwasting properties of the resources and economic assumption of Kaldor. The important results of this study contain the notions of bounded solutions, the existence of an attractive set, local and global stability of equilibrium, the system permanence, and the existence of a limit cycle.

  8. Cyclic Growth and Global Stability of Economic Dynamics of Kaldor Type in Two Dimensions

    Nindjin, Aka Fulgence; N’Guessan, Albin Tetchi; Okou, Hypolithe; Tia, Kessé Thiban
    This article proposes nonlinear economic dynamics continuous in two dimensions of Kaldor type, the saving rate and the investment rate, which are functions of ecological origin verifying the nonwasting properties of the resources and economic assumption of Kaldor. The important results of this study contain the notions of bounded solutions, the existence of an attractive set, local and global stability of equilibrium, the system permanence, and the existence of a limit cycle.

  9. Cyclic Growth and Global Stability of Economic Dynamics of Kaldor Type in Two Dimensions

    Nindjin, Aka Fulgence; N’Guessan, Albin Tetchi; Okou, Hypolithe; Tia, Kessé Thiban
    This article proposes nonlinear economic dynamics continuous in two dimensions of Kaldor type, the saving rate and the investment rate, which are functions of ecological origin verifying the nonwasting properties of the resources and economic assumption of Kaldor. The important results of this study contain the notions of bounded solutions, the existence of an attractive set, local and global stability of equilibrium, the system permanence, and the existence of a limit cycle.

  10. Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

    Atifi, K.; Balouki, Y.; Essoufi, El-H.; Khouiti, B.
    A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a...

  11. Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

    Atifi, K.; Balouki, Y.; Essoufi, El-H.; Khouiti, B.
    A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov...

  12. Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

    Atifi, K.; Balouki, Y.; Essoufi, El-H.; Khouiti, B.
    A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we...

  13. Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations

    Isah, Abdulnasir; Phang, Chang; Phang, Piau
    An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool...

  14. Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations

    Isah, Abdulnasir; Phang, Chang; Phang, Piau
    An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding...

  15. Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations

    Isah, Abdulnasir; Phang, Chang; Phang, Piau
    An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows...

  16. On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

    Iyase, S. A.; Imaga, O. F.
    The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments.

  17. On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

    Iyase, S. A.; Imaga, O. F.
    The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments.

  18. On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

    Iyase, S. A.; Imaga, O. F.
    The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments.

  19. Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points

    Lukashiv, Taras; Malyk, Igor
    In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example.

  20. Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points

    Lukashiv, Taras; Malyk, Igor
    In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example.

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