• 제목/요약/키워드: two point boundary value problems

검색결과 57건 처리시간 0.02초

A FIFTH ORDER NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • 제26권3_4호
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    • pp.689-706
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    • 2008
  • In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

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POSITIVE SOLUTIONS OF SINGULAR FOURTH-ORDER TWO POINT BOUNDARY VALUE PROBLEMS

  • Li, Jiemei
    • Journal of applied mathematics & informatics
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    • 제27권5_6호
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    • pp.1361-1370
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    • 2009
  • In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.

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Existence and Uniqueness Theorems for Certain Fourth-order Boundary Value Problems

  • Minghe, Pei;Chang, Sung Kag
    • Kyungpook Mathematical Journal
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    • 제45권3호
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    • pp.349-356
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    • 2005
  • In this paper, by using the Leray-Schauder continuation theorem and Wirtinger-type inequalities, we establish the existence and uniqueness theorems for two-point boundary value problems of a certain class of fourth-order nonlinear differential equations.

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FUNCTIONAL ITERATIVE METHODS FOR SOLVING TWO-POINT BOUNDARY VALUE PROBLEMS

  • Lim, Hyo Jin;Kim, Kyoum Sun;Yun, Jae Heon
    • Journal of applied mathematics & informatics
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    • 제31권5_6호
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    • pp.733-745
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    • 2013
  • In this paper, we first propose a new technique of the functional iterative methods VIM (Variational iteration method) and NHPM (New homotopy perturbation method) for solving two-point boundary value problems, and then we compare their numerical results with those of the finite difference method (FDM).

ON DICHOTOMY AND CONDITIONING FOR TWO-POINT BOUNDARY VALUE PROBLEMS ASSOCIATED WITH FIRST ORDER MATRIX LYAPUNOV SYSTEMS

  • Murty, M.S.N.;Kumar, G. Suresh
    • 대한수학회지
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    • 제45권5호
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    • pp.1361-1378
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    • 2008
  • This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS ARISING IN CHEMICAL REACTOR THEORY

  • Andargie, Awoke
    • Journal of applied mathematics & informatics
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    • 제28권1_2호
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    • pp.411-423
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    • 2010
  • In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

NUMERICAL INTEGRATION METHOD FOR SINGULAR PERTURBATION PROBLEMS WITH MIXED BOUNDARY CONDITIONS

  • Andargie, Awoke;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • 제26권5_6호
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    • pp.1273-1287
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    • 2008
  • In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

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EXISTENCE OF SOLUTIONS OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS FOR 2NTH-ORDER NONLINEAR DIFFERENTIAL EQUATION

  • Gao, Yongxin;Wang, Renfei
    • Journal of applied mathematics & informatics
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    • 제27권5_6호
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    • pp.1465-1472
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    • 2009
  • In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

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THREE POINT BOUNDARY VALUE PROBLEMS FOR THIRD ORDER FUZZY DIFFERENTIAL EQUATIONS

  • Murty, M.S.N.;Kumar, G. Suresh
    • 충청수학회지
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    • 제19권1호
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    • pp.101-110
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    • 2006
  • In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green's functions and contraction mapping principle.

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THE METHOD OF ASYMPTOTIC INNER BOUNDARY CONDITION FOR SINGULAR PERTURBATION PROBLEMS

  • Andargie, Awoke;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • 제29권3_4호
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    • pp.937-948
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    • 2011
  • The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.