메뉴 건너뛰기




Volumn 39, Issue 2, 2009, Pages 125-154

A fictitious time integration method for solving m-point boundary value problems

Author keywords

Euler Bernoulli beam; Fictitious Time Integration Method (FTIM); Multi point boundary value problems; Periodic solution

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; NONLINEAR EQUATIONS; VIBRATION MEASUREMENT;

EID: 63349084543     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (25)

References (56)
  • 1
    • 0018441912 scopus 로고
    • The numerical solution of multipoint boundary value problems
    • Agarwal, R. P. (1979): The numerical solution of multipoint boundary value problems. Journal of Computational and Applied Mathematics, vol. 5, pp. 17-24.
    • (1979) Journal of Computational and Applied Mathematics , vol.5 , pp. 17-24
    • Agarwal, R.P.1
  • 2
    • 52449113563 scopus 로고    scopus 로고
    • Generalized quasilinearization method for a second-order three point boundary-value problem with nonlinear boundary conditions
    • Ahmad, B.; Ali Khan, R.; Eloe, P. W. (2002): Generalized quasilinearization method for a second-order three point boundary-value problem with nonlinear boundary conditions. Electric Journal of Differential Equations, vol. 2002, pp. 1-12.
    • (2002) Electric Journal of Differential Equations , vol.2002 , pp. 1-12
    • Ahmad, B.1    Ali Khan, R.2    Eloe, P.W.3
  • 4
    • 41949129777 scopus 로고    scopus 로고
    • Global behavior of the components for the second order m-point boundary value problems
    • Article ID
    • An, Y.; Ma, R. (2008): Global behavior of the components for the second order m-point boundary value problems. Boundary Value Problems, vol. 2008, Article ID 254593.
    • (2008) Boundary Value Problems , vol.2008 , pp. 254593
    • An, Y.1    Ma, R.2
  • 6
    • 52449120338 scopus 로고    scopus 로고
    • Existence of positive solutions for fourth-order three-point boundary value problems
    • Article ID 68758
    • Bai, C. (2007): Existence of positive solutions for fourth-order three-point boundary value problems. Boundary Value Problems, vol. 2007, Article ID 68758.
    • (2007) Boundary Value Problems , vol.2007
    • Bai, C.1
  • 7
    • 34247324882 scopus 로고
    • Orbit determination as a multipoint boundary-value problem and quasilinearization
    • Bellman, R.; Kagiwada, H.; Kalába, R. (1962); Orbit determination as a multipoint boundary-value problem and quasilinearization. Mathematics, vol. 48, pp. 1327-1329.
    • (1962) Mathematics , vol.48 , pp. 1327-1329
    • Bellman, R.1    Kagiwada, H.2    Kalába, R.3
  • 8
    • 34848865658 scopus 로고    scopus 로고
    • Numerical solution of a singularly perturbed three-point boundary value problem
    • Cakir, M.; Amiraliyev, G. M. (2007): Numerical solution of a singularly perturbed three-point boundary value problem. International Journal of Computer Mathematics, vol. 84, pp. 1465-1481.
    • (2007) International Journal of Computer Mathematics , vol.84 , pp. 1465-1481
    • Cakir, M.1    Amiraliyev, G.M.2
  • 9
    • 14744292817 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to a superlinear three-point boundary-value problem
    • Calvert, B.; Gupta, C. P. (2005): Existence and uniqueness of solutions to a superlinear three-point boundary-value problem. Electric Journal of Differential Equations, vol. 2005, pp. 1-21.
    • (2005) Electric Journal of Differential Equations , vol.2005 , pp. 1-21
    • Calvert, B.1    Gupta, C.P.2
  • 10
    • 0022791144 scopus 로고
    • On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, Part 1: A survey and comparison of some one-step formulae
    • Cash, J. R. (1986): On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, Part 1: a survey and comparison of some one-step formulae. Computer and Mathematics with Applications, vol. 12, pp. 1029-1048.
    • (1986) Computer and Mathematics with Applications , vol.12 , pp. 1029-1048
    • Cash, J.R.1
  • 11
    • 0000257129 scopus 로고
    • On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, Part 2: The development and analysis of highly stable deferred correction formulae
    • Cash, J. R. (1988): On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, Part 2: the development and analysis of highly stable deferred correction formulae. SIAM Journal on Numerical Analysis, vol. 25, pp. 862-882.
    • (1988) SIAM Journal on Numerical Analysis , vol.25 , pp. 862-882
    • Cash, J.R.1
  • 12
    • 0032182567 scopus 로고    scopus 로고
    • Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems
    • Cash, J. R.; Wright, R. W. (1998): Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems. Applied Numerical Mathematics, vol. 28, pp. 227-244.
    • (1998) Applied Numerical Mathematics , vol.28 , pp. 227-244
    • Cash, J.R.1    Wright, R.W.2
  • 13
    • 49749148437 scopus 로고    scopus 로고
    • The Lie-group shooting method for solving classical Blasius flat-plate problem
    • Chang, C. W.; Chang, J. R.; Liu, C.-S. (2008): The Lie-group shooting method for solving classical Blasius flat-plate problem. CMC: Computers, Materials & Continua, vol. 7, pp. 139-153.
    • (2008) CMC: Computers, Materials & Continua , vol.7 , pp. 139-153
    • Chang, C.W.1    Chang, J.R.2    Liu, C.-S.3
  • 14
    • 33847712471 scopus 로고    scopus 로고
    • A new shooting method for quasi-boundary regularization of backward heat conduction problems
    • Chang, J. R.; Liu, C.-S.; Chang, C. W. (2007); A new shooting method for quasi-boundary regularization of backward heat conduction problems. International Journal of Heat and Mass Transfer, vol. 50, pp. 2325-2332.
    • (2007) International Journal of Heat and Mass Transfer , vol.50 , pp. 2325-2332
    • Chang, J.R.1    Liu, C.-S.2    Chang, C.W.3
  • 15
    • 41949104996 scopus 로고    scopus 로고
    • A numerical approach to nonlinear two-point boundary value problems for ODEs
    • Cuomo, S.; Marasco, A. (2008): A numerical approach to nonlinear two-point boundary value problems for ODEs. Computer and Mathematics with Applications, vol. 55, pp. 2476-2489.
    • (2008) Computer and Mathematics with Applications , vol.55 , pp. 2476-2489
    • Cuomo, S.1    Marasco, A.2
  • 16
    • 0005338184 scopus 로고    scopus 로고
    • An algorithm for solving boundary value problems
    • Deeba, E.; Khuri, S. A.; Xie, S. (2000): An algorithm for solving boundary value problems. Journal of Computational Physics, vol. 159, pp. 125-138.
    • (2000) Journal of Computational Physics , vol.159 , pp. 125-138
    • Deeba, E.1    Khuri, S.A.2    Xie, S.3
  • 17
    • 43149087062 scopus 로고    scopus 로고
    • Solvability for two classes of higher-order multi-point boundary value problems at resonance
    • Article ID
    • Gao, Y.; Pei, M. (2008): Solvability for two classes of higher-order multi-point boundary value problems at resonance. Boundary Value Problems, vol. 2008, Article ID 723828.
    • (2008) Boundary Value Problems , vol.2008 , pp. 723828
    • Gao, Y.1    Pei, M.2
  • 18
    • 0019008419 scopus 로고
    • Improved shooting techniques for linear boundary value problems
    • Garg, V. K. (1980): Improved shooting techniques for linear boundary value problems. Computer Methods in Applied Mechanics and Engineering, vol. 22, pp. 87-99.
    • (1980) Computer Methods in Applied Mechanics and Engineering , vol.22 , pp. 87-99
    • Garg, V.K.1
  • 19
    • 0001070154 scopus 로고
    • Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation
    • Gupta, C. P. (1992): Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. Journal of Mathematical Analysis and Applications, vol. 168, pp. 540-551.
    • (1992) Journal of Mathematical Analysis and Applications , vol.168 , pp. 540-551
    • Gupta, C.P.1
  • 20
    • 0000830764 scopus 로고
    • A note on a second order three-point nonlinear boundary value problem
    • Gupta, C. P. (1994): A note on a second order three-point nonlinear boundary value problem. Journal of Mathematical Analysis and Applications, vol. 186, pp. 277-281.
    • (1994) Journal of Mathematical Analysis and Applications , vol.186 , pp. 277-281
    • Gupta, C.P.1
  • 21
    • 0035500967 scopus 로고    scopus 로고
    • A nonlinear shooting method for two-point boundary value problems
    • Ha, S. N. (2001): A nonlinear shooting method for two-point boundary value problems. Computer and Mathematics with Applications, vol. 42, pp. 1411-1420.
    • (2001) Computer and Mathematics with Applications , vol.42 , pp. 1411-1420
    • Ha, S.N.1
  • 22
    • 0036902754 scopus 로고    scopus 로고
    • Numerical study for two-point boundary value problems using Green's functions
    • Ha, S. N.; Lee, C. R. (2002): Numerical study for two-point boundary value problems using Green's functions. Computer and Mathematics with Applications, vol. 44, pp. 1599-1608.
    • (2002) Computer and Mathematics with Applications , vol.44 , pp. 1599-1608
    • Ha, S.N.1    Lee, C.R.2
  • 23
    • 5344232128 scopus 로고    scopus 로고
    • Double solutions of three-point boundary-value problems for second-order differential equations
    • Henderson, J. (2004): Double solutions of three-point boundary-value problems for second-order differential equations. Electric Journal of Differential Equations, vol. 2004, pp. 1-7.
    • (2004) Electric Journal of Differential Equations , vol.2004 , pp. 1-7
    • Henderson, J.1
  • 24
    • 52449097466 scopus 로고    scopus 로고
    • Several existence theorems of monotone positive solutions for third-order multipoint boundary value problems
    • Article ID 17951
    • Jiang, W.; Li, F. (2007): Several existence theorems of monotone positive solutions for third-order multipoint boundary value problems. Boundary Value Problems, vol. 2007, Article ID 17951.
    • (2007) Boundary Value Problems , vol.2007
    • Jiang, W.1    Li, F.2
  • 27
    • 33744827372 scopus 로고    scopus 로고
    • The shooting method and multiple solutions of two/multipoint BVPs of second order ODE
    • Kwong, M. K. (2006): The shooting method and multiple solutions of two/multipoint BVPs of second order ODE. Electric Journal of Qualitative Theory of Differential Equations, vol. 2006, pp. 1-14.
    • (2006) Electric Journal of Qualitative Theory of Differential Equations , vol.2006 , pp. 1-14
    • Kwong, M.K.1
  • 28
    • 38849095711 scopus 로고    scopus 로고
    • The shooting method and nonhomogeneous multipoint BVPs of second-order ODE
    • Article ID 64012
    • Kwong, M. K.; Wong, J. S. (2007): The shooting method and nonhomogeneous multipoint BVPs of second-order ODE. Boundary Value Problems, vol. 2007, Article ID 64012.
    • (2007) Boundary Value Problems , vol.2007
    • Kwong, M.K.1    Wong, J.S.2
  • 29
    • 3042521066 scopus 로고    scopus 로고
    • A method to determine the periodic solution of the non-linear dynamics system
    • Li, D.; Xu, J. (2004): A method to determine the periodic solution of the non-linear dynamics system. Journal of Sound and Vibration, vol. 275, pp. 1-16.
    • (2004) Journal of Sound and Vibration , vol.275 , pp. 1-16
    • Li, D.1    Xu, J.2
  • 30
    • 0035480574 scopus 로고    scopus 로고
    • Cone of non-linear dynamical system and group preserving schemes
    • Liu, C.-S. (2001): Cone of non-linear dynamical system and group preserving schemes. International Journal of Non-Linear Mechanics, vol. 36, pp. 1047-1068.
    • (2001) International Journal of Non-Linear Mechanics , vol.36 , pp. 1047-1068
    • Liu, C.-S.1
  • 31
    • 33744980037 scopus 로고    scopus 로고
    • The Lie-group shooting method for nonlinear two-point boundary value problems exhibiting multiple solutions
    • Liu, C.-S. (2006a): The Lie-group shooting method for nonlinear two-point boundary value problems exhibiting multiple solutions. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp. 149-163.
    • (2006) CMES: Computer Modeling in Engineering & Sciences , vol.13 , pp. 149-163
    • Liu, C.-S.1
  • 32
    • 33845426680 scopus 로고    scopus 로고
    • Efficient shooting methods for the second order ordinary differential equations
    • Liu, C.-S. (2006b): Efficient shooting methods for the second order ordinary differential equations. CMES: Computer Modeling in Engineering & Sciences, vol. 15, pp. 69-86.
    • (2006) CMES: Computer Modeling in Engineering & Sciences , vol.15 , pp. 69-86
    • Liu, C.-S.1
  • 33
    • 33845427623 scopus 로고    scopus 로고
    • The Lie-group shooting method for singularly perturbed two-point boundary value problems
    • Liu, C.-S. (2006c): The Lie-group shooting method for singularly perturbed two-point boundary value problems. CMES: Computer Modeling in Engineering & Sciences, vol. 15, pp. 179-196.
    • (2006) CMES: Computer Modeling in Engineering & Sciences , vol.15 , pp. 179-196
    • Liu, C.-S.1
  • 34
    • 52449088249 scopus 로고    scopus 로고
    • A two-stage LGSM for three-point BVPs of second-order ODEs
    • Article ID 963753, 22 pages
    • Liu, C.-S. (2008a): A two-stage LGSM for three-point BVPs of second-order ODEs. Boundary Value Problems, vol. 2008, Article ID 963753, 22 pages.
    • (2008) Boundary Value Problems , vol.2008
    • Liu, C.-S.1
  • 35
    • 41649113492 scopus 로고    scopus 로고
    • An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature
    • Liu, C.-S. (2008b): An LGSM to identify nonhomogeneous heat conductivity functions by an extra measurement of temperature. International Journal of Heat and Mass Transfer, vol. 51, pp. 2603-2613.
    • (2008) International Journal of Heat and Mass Transfer , vol.51 , pp. 2603-2613
    • Liu, C.-S.1
  • 36
    • 46449098515 scopus 로고    scopus 로고
    • An LGEM to identify time-dependent heat conductivity function by an extra measurement of temperature gradient
    • Liu, C.-S. (2008c): An LGEM to identify time-dependent heat conductivity function by an extra measurement of temperature gradient. CMC: Computers, Materials & Continua, vol. 7, pp. 81-95.
    • (2008) CMC: Computers, Materials & Continua , vol.7 , pp. 81-95
    • Liu, C.-S.1
  • 37
    • 43049107224 scopus 로고    scopus 로고
    • Solving an inverse Sturm-Liouville problem by a Lie-group method
    • Article ID 749865, 18 pages
    • Liu, C.-S. (2008d): Solving an inverse Sturm-Liouville problem by a Lie-group method. Boundary Value Problems, vol. 2008, Article ID 749865, 18 pages.
    • (2008) Boundary Value Problems , vol.2008
    • Liu, C.-S.1
  • 38
    • 46449129207 scopus 로고    scopus 로고
    • Identifying time-dependent damping and stiffness functions by a simple and yet accurate method
    • Liu, C.-S. (2008e): Identifying time-dependent damping and stiffness functions by a simple and yet accurate method. Journal of Sound and Vibration, vol. 318, pp. 148-165.
    • (2008) Journal of Sound and Vibration , vol.318 , pp. 148-165
    • Liu, C.-S.1
  • 39
    • 49149112956 scopus 로고    scopus 로고
    • A Lie-group shooting method for simultaneously estimating the time-dependent damping and stiffness coefficients
    • Liu, C.-S. (2008f): A Lie-group shooting method for simultaneously estimating the time-dependent damping and stiffness coefficients. CMES: Computer Modeling in Engineering & Sciences, vol. 27, pp. 137-149.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.27 , pp. 137-149
    • Liu, C.-S.1
  • 40
    • 58149514376 scopus 로고    scopus 로고
    • A Lie-group shooting method estimating nonlinear restoring forces in mechanical systems
    • Liu, C.-S. (2008g): A Lie-group shooting method estimating nonlinear restoring forces in mechanical systems. CMES: Computer Modeling in Engineering & Sciences, vol. 35, pp. 157-180.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.35 , pp. 157-180
    • Liu, C.-S.1
  • 41
    • 58149396461 scopus 로고    scopus 로고
    • A time-marching algorithm for solving non-linear obstacle problems with the aid of an NCP-function
    • Liu, C.-S. (2008h): A time-marching algorithm for solving non-linear obstacle problems with the aid of an NCP-function. CMC: Computers, Materials & Continua, vol. 8, pp. 53-65.
    • (2008) CMC: Computers, Materials & Continua , vol.8 , pp. 53-65
    • Liu, C.-S.1
  • 42
    • 57349138589 scopus 로고    scopus 로고
    • A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems
    • Liu, C.-S. (2008i): A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems. CMES: Computer Modeling in Engineering & Sciences, vol. 33, pp. 179-198.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.33 , pp. 179-198
    • Liu, C.-S.1
  • 43
    • 55349116390 scopus 로고    scopus 로고
    • A novel time integration method for solving a large system of non-linear algebraic equations
    • Liu, C.-S.; Atluri, S. N. (2008a): A novel time integration method for solving a large system of non-linear algebraic equations. CMES: Computer Modeling in Engineering & Sciences, vol. 31, pp. 71-83.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.31 , pp. 71-83
    • Liu, C.-S.1    Atluri, S.N.2
  • 44
    • 57649213675 scopus 로고    scopus 로고
    • A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization
    • Liu, C.-S.; Atluri, S. N. (2008b): A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization. CMES: Computer Modeling in Engineering & Sciences, vol. 34, pp. 155-178.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.34 , pp. 155-178
    • Liu, C.-S.1    Atluri, S.N.2
  • 47
    • 46449109059 scopus 로고    scopus 로고
    • Simultaneously estimating the time-dependent damping and stiffness coefficients with the aid of vibrational data
    • Liu, C.-S.; Chang, J. R.; Chang, K. H.; Chen, Y. W. (2008): Simultaneously estimating the time-dependent damping and stiffness coefficients with the aid of vibrational data. CMC: Computers, Materials & Continua, vol. 7, pp. 97-107.
    • (2008) CMC: Computers, Materials & Continua , vol.7 , pp. 97-107
    • Liu, C.-S.1    Chang, J.R.2    Chang, K.H.3    Chen, Y.W.4
  • 48
    • 14744305428 scopus 로고    scopus 로고
    • Positive solutions to a generalized second-order three-point boundary value problem on time scales
    • Luo, H.; Ma, Q. (2005): Positive solutions to a generalized second-order three-point boundary value problem on time scales. Electric Journal of Differential Equations, vol. 2005, pp. 1-14.
    • (2005) Electric Journal of Differential Equations , vol.2005 , pp. 1-14
    • Luo, H.1    Ma, Q.2
  • 49
    • 0001333843 scopus 로고    scopus 로고
    • Positive solutions of a nonlinear three-point boundary-value problem
    • Ma, R. (1998): Positive solutions of a nonlinear three-point boundary-value problem. Electric Journal of Differential Equations, vol. 1998, pp. 1-8.
    • (1998) Electric Journal of Differential Equations , vol.1998 , pp. 1-8
    • Ma, R.1
  • 50
    • 34248190802 scopus 로고    scopus 로고
    • A three-point boundary value problem with an integral two-space-variables condition for parabolic equations
    • Marhoune, A. L. (2006): A three-point boundary value problem with an integral two-space-variables condition for parabolic equations. Computer and Mathematics with Applications, vol. 53, pp. 940-947.
    • (2006) Computer and Mathematics with Applications , vol.53 , pp. 940-947
    • Marhoune, A.L.1
  • 51
    • 0042140702 scopus 로고    scopus 로고
    • Modified potentials as a tool for computing Green's functions in continuum mechanics
    • Melnikov, Y. A.; Melnikov, M. Y. (2001): Modified potentials as a tool for computing Green's functions in continuum mechanics. CMES: Computer Modeling in Engineering & Sciences, vol. 2, pp. 291-306.
    • (2001) CMES: Computer Modeling in Engineering & Sciences , vol.2 , pp. 291-306
    • Melnikov, Y.A.1    Melnikov, M.Y.2
  • 52
    • 0023329415 scopus 로고
    • Modified deflation algorithm for the solution of singular problems. II. nonlinear multipoint boundary value problems
    • Ojika, T. (1987): Modified deflation algorithm for the solution of singular problems. II. nonlinear multipoint boundary value problems. Journal of Mathematical Analysis and Applications, vol. 123, pp. 222-237.
    • (1987) Journal of Mathematical Analysis and Applications , vol.123 , pp. 222-237
    • Ojika, T.1
  • 53
    • 0018479694 scopus 로고
    • Initial-value adjusting method for the solution of nonlinear multipoint boundary-value problems
    • Ojika, T.; Kasue, Y. (1979): Initial-value adjusting method for the solution of nonlinear multipoint boundary-value problems. Journal of Mathematical Analysis and Applications, vol. 69, pp. 359-371.
    • (1979) Journal of Mathematical Analysis and Applications , vol.69 , pp. 359-371
    • Ojika, T.1    Kasue, Y.2
  • 54
    • 38949209871 scopus 로고    scopus 로고
    • Existence of symmetric positive solutions for an m-point boundary value problem
    • Article ID 79090
    • Sun, Y.; Zhang, X. (2007): Existence of symmetric positive solutions for an m-point boundary value problem. Boundary Value Problems, vol. 2007, Article ID 79090.
    • (2007) Boundary Value Problems , vol.2007
    • Sun, Y.1    Zhang, X.2
  • 55
    • 0003066387 scopus 로고    scopus 로고
    • The global bifurcation characteristics of the forced van der Pol oscillator
    • Xu, J.; Jiang, J. (1996): The global bifurcation characteristics of the forced van der Pol oscillator. Chaos Solitons and Fractals, vol. 7, pp. 3-19.
    • (1996) Chaos Solitons and Fractals , vol.7 , pp. 3-19
    • Xu, J.1    Jiang, J.2
  • 56
    • 33846661305 scopus 로고    scopus 로고
    • Positive solutions for singular three-point boundary-value problems
    • Zhao, Z. (2007): Positive solutions for singular three-point boundary-value problems. Electric Journal of Differential Equations, vol. 2007, pp. 1-8.
    • (2007) Electric Journal of Differential Equations , vol.2007 , pp. 1-8
    • Zhao, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.