A finite difference method for the numerical solving general third-order boundary-value problem with an internal boundary condition
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 35-45.

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In this paper we have proposed a finite difference method for the numerical solving general third-order boundary-value problem. Under appropriate conditions we have discussed the convergence of the proposed method. The computational results in experiment on test problems verify the efficiency and theoretically established second order accuracy of the proposed method.
Keywords: boundary-value problem, difference method, nonlinear, second order sonvergence, three-point BVP.
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     author = {P. K. Pandey},
     title = {A finite difference method for the numerical solving general third-order boundary-value problem with an internal boundary condition},
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}
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P. K. Pandey. A finite difference method for the numerical solving general third-order boundary-value problem with an internal boundary condition. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 35-45. http://geodesic.mathdoc.fr/item/IVM_2017_12_a3/

[1] Gregus M., Third order linear differential equations, Math. and Appl. (East European Series), D. Reidel Publ. Company, Dordrecht–Boston–Lancaster–Tokyo, 1987 | MR | Zbl

[2] Jackson L. K., “Existence and uniqueness of solutions of boundary-value problems for third order differential equations”, J. Diff. Eqs., 13 (1973), 432–437 | DOI | MR | Zbl

[3] Gupta C. P., Lakshmikantham V., “Existence and uniqueness theorems for a third-order three point boundary-value problem”, Nonlinear Analysis: Theory, Methods Appl., 16:11 (1991), 949–957 | DOI | MR | Zbl

[4] Murty K. N., Rao Y. S., “A theory for existence and uniqueness of solutions to three-point boundary-value problems”, J. Math. Anal. and Appl., 167:1 (1992), 43–48 | DOI | MR | Zbl

[5] Henderson J., Prasad K. R., “Existence and uniqueness of solutions of three-point boundary-value problems on time scales”, Nonlin. Studies, 8 (2001), 1–12 | MR | Zbl

[6] Gregus M., Abdel Karim R. I. I., “Boundedness of the solutions of the differential equation $(py')'' + (py')' + ry = 0 $”, Proc. Math. and Phys. Soc., U.A.R., 32 (1968), 107–110 | MR | Zbl

[7] Agarwal R. P., Boundary-value problems for higher order differential equations, World Scientific, Singapore, 1986 | MR | Zbl

[8] Na T. Y., Computational methods in engineering boundary-value problems, Academic Press, New York, 1979 | MR | Zbl

[9] Al-Said E. A., “Numerical solutions for system of third-order boundary-value problems”, International J. Computer Math., 78:1 (2001), 111–121 | DOI | MR | Zbl

[10] Khan A., Aziz T., “The numerical solution of third-order boundary-value problems using quintic splines”, Appl. Math. and Comput., 137:2–3 (2003), 253–260 | MR | Zbl

[11] Islam S., Khan M. A., Tirmizi I. A., Twizell E. H., “Non-polynomial splines approach to the solution of a system of third-order boundary-value problems”, Appl. Math. and Comput., 168:1 (2005), 152–163 | MR | Zbl

[12] Li X., Wu B., “Reproducing kernel method for singular multi-point boundary-value problems”, Math. Sci., 6 (2012), 16 | DOI | MR

[13] Pandey P. K., “The numerical solution of third order differential equation containing the first derivative”, Neural Parallel Scientific Comp., 13 (2005), 297–304 | MR | Zbl

[14] Varga R. S., Matrichnyi iteratsionnyi analiz, Springer-Verlag, Heidelberg, 2002

[15] Horn R. A., Johnson C. R., Matrix analysis, Cambridge University Press, New York, NY1, USA, 1001 | MR

[16] Jator S. N., “On the numerical integration of third order boundary-value problems by a linear multistep method”, International J. Pure and Appl. Math., 46:3 (2008), 375–388 | MR | Zbl

[17] Krajcinovic D., “Sandwich beam analysis”, J. Appl. Mech., 1971, 773–778

[18] Ghazala A., Muhammad T., Shahid S. S., Hamood U. R., “Solution of a linear third order multi-point boundary value problem using RKM”, British J. Math. Comp. Sci., 3:2 (2013), 180–194 | DOI