Exact three-point difference scheme for a nonlinear boundary-value problem on the semiaxis

Kutniv, M.; Pazdrii, O.
March 2012
Journal of Mathematical Sciences;Mar2012, Vol. 181 Issue 3, p383
Academic Journal
For the numerical solution of boundary-value problems on the semiaxis for second-order nonlinear ordinary differential equations, an exact three-point difference scheme is constructed and substantiated. Under the conditions of existence and uniqueness of solution of a boundary-value problem, we prove the existence and uniqueness of solution of the exact three-point difference scheme and convergence of the method of successive approximations for its solution.


Related Articles

  • Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space. Xueqin Lü; Minggen Cui // Boundary Value Problems;2010, Special section p1 

    We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given underweaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using...

  • Differential inclusions and optimization problem on time scales. Miranda, Francisco // AIP Conference Proceedings;Sep2012, Vol. 1479 Issue 1, p745 

    In this paper, we present conditions of existence of solution to an optimization problem on time scales. Based on the classical results for continuous-time case, a convergence theorem for delta-differential inclusions is proved. It is applied to establish an existence results for an optimization...

  • Solvability of Nonlocal Fractional Boundary Value Problems. Zhongmin Huang; Chengmin Hou // Discrete Dynamics in Nature & Society;2013, p1 

    This paper is devoted to introduce a new approach to investigate the existence of solutions for a three-point boundary value problem of fractional difference equations as fllows: Δ vy(t) = f(t + v - 1, y(t + v - 1), Δy(t + v - 2)), y(v - 2) = 0, and [Δαy(t)]t=v+b-α+1 =...

  • Existence of solutions and estimates of the velocity of convergence of approximate solutions of nonclassical type nonlinear degenerate equation. Muratbekov, Mussakan B.; Shyrakbaev, Abai B.; Suleimbekova, Ainash O. // AIP Conference Proceedings;2014, Vol. 1611, p105 

    This paper is devoted to the existence, smoothness and approximative properties of solutions of the semiperiodical Dirichlet problem of a class of nonclassical type degenerate nonlinear equations.

  • Elliptic p-Laplacian Equations with Indefinite Concave Nonlinearities near the Origin. Afrouzi, G. A.; Bai, M. // Advances in Theoretical & Applied Mathematics;2012, Vol. 7 Issue 1, p51 

    In this note existence of infinitely many solutions is proved for an elliptic p-Laplacian equation with indefinite concave nonlinearities.

  • Boundary value problems for fractional q-difference equations with nonlocal conditions. Xinhui Li; Zhenlai Han; Shurong Sun; Hongling Lu // Advances in Difference Equations;Feb2014, Vol. 2014, p1 

    In this paper, we study the boundary value problem of a fractional q-difference equation with nonlocal conditions involving the fractional q-derivative of the Caputo type, and the nonlinear term contains a fractional q-derivative of Caputo type. By means of Bananch's contraction mapping...

  • A Periodic Problem of a Semilinear Pseudoparabolic Equation. Yang Cao; Jingxue Yin; Chunhua Jin // Abstract & Applied Analysis;2011, Special section p1 

    A class of periodic problems of pseudoparabolic type equations with nonlinear periodic sources are investigated. A rather complete classification of the exponent p is given, in terms of the existence and nonexistence of nontrivial and nonnegative periodic solutions.

  • ON A SYSTEM OF HIGHER-ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS. Henderson, Johnny; Luca, Rodica // Electronic Journal of Qualitative Theory of Differential Equatio;2012, Issue 50-74, p1 

    We investigate the existence and nonexistence of positive solutions for a system of nonlinear higher-order ordinary differential equations subject to some multi-point boundary conditions.

  • Nonlinear equations with essentially infinite-dimensional differential operators. Bohdans'kyi, Yu.; Statkevych, V. // Ukrainian Mathematical Journal;Apr2011, Vol. 62 Issue 11, p1822 

    We consider nonlinear differential equations and boundary-value problems with essentially infinite-dimensional operators (of the Laplace-Lévy type). An analog of the Picard theorem is proved.


Read the Article

Courtesy of

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics