A Subdivision Approach to the Approximate Solution of 3rd Order Boundary Value Problem

S. A. Manan, A. Ghaffar, M. Rizwan, G. Rahman, G. Kanwal


An algorithm to solve 3rd order boundary value problem is focused in this paper which is 8-point approximating scheme. It concludes the results with stability and convergence that is evaluated with the illustration of numerical example. This paper also contains the analysis of approximation properties for the mentioned collocation algorithm.


Subdivision scheme; Boundary value problem; Convergence; Stability

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M. Aslam, G. Mustafa and A. Ghaffar, (2n-1)-Point ternary approximating and interpolating subdivision schemes, Journal of Applied Mathematics 2011 (2011), Article ID 832630, 13 pages, DOI: 10.1155/2011/832630.

G. de Rham, Sur une courbe plane, Journal de Mathématiques Pures et Appliquées 35 (1956), 25 – 42.

N. Dyn, D. Levin and J.A. Gregory, A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design 4(4) (1987), 257 – 268.

N. Dyn, M.S. Floater and K. Hormann, A C2 four-point subdivision scheme with fourth order accuracy and its extensions, Analysis 1(128) (2005), f2.

A. Ghaffar, G. Mustafa and K. Qin, Unification and application of 3-point approximating subdivision schemes of varying arity, Open Journal of Applied Sciences 2(4b) (2012), 48 – 52.

A. Ghaffar and G. Mustafa, A family of even-point ternary approximating schemes, ISRN Applied Mathematics 2012 (2012), Article ID 197383, 14 pages, DOI: 10.5402/2012/197383.

G. Mustafa, F. Khan and A. Ghaffar, The m-point approximating subdivision scheme, Lobachevskii Journal of Mathematics 30(2) (2009), 138 – 145.

G. Mustafa and S.T. Ejaz, Numerical solution of two-point boundary value problems by interpolating subdivision schemes, Abstract and Applied Analysis 2014 (2014), Article ID 721314, 13 pages, DOI: 10.1155/2014/721314.

G. Mustafa, M. Abbas, S.T. Ejaz, A.I.M. Ismail and F. Khan, A numerical approach based on subdivision schemes for solving non-linear fourth order boundary value problems, Journal of Computational Analysis & Applications 23(1) (2017), 607 – 623.

G. Mustafa and S.T. Ejaz, A subdivision collocation method for solving two point boundary value problems of order three, Journal of Applied Analysis and Computation 7(3) (2017), 942 – 956.

R. Qu, Curve and surface interpolation by subdivision algorithms, Comput. Aided Drafting, Des. Manufact. 4(2) (1994), 28 – 39.

R. Qu and R.P. Agarwal, A cross difference approach to the analysis of subdivision algorithms, Neural, Parallel & Scientific Computations 3(3) (1995), 393 – 416.

R. Qu and R.P. Agarwal, Solving two point boundary value problems by interpolatory subdivision algorithms, International Journal of Computer Mathematics 60(3-4) (1996), 279 – 294.

R. Qu and R.P. Agarwal, A subdivision approach to the construction of approximate solutions of boundary-value problems with deviating arguments, Computers & Mathematics with Applications 35(11) (1998), 121 – 135.

E. Quak and M.S. Floater, Tutorials on Multiresolution in Geometric Modelling: Summer School Lectures Notes, Springer-Verlag New York, Inc. (2002).

W. Us Salam, S.S. Siddiqi and K. Rehan, Chaikin’s perturbation subdivision scheme in nonstationary forms, Alexandria Engineering Journal 55(3) (2016), 2855 – 2862.

DOI: http://dx.doi.org/10.26713%2Fcma.v9i4.835


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