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The numerical solution of third-order boundary-value problems using quintic splines. (English) Zbl 1027.65100

Summary: We present a fourth-order method based on quintic splines for the solution of third-order linear and nonlinear boundary-value problems (BVPs) of the form \(y'''=f(x,y),a\leqslant x\leqslant b\), subject to the boundary conditions \(y(a)=k_1, y'(a)=k_2, y(b)=k_3\). Numerical examples are given to illustrate the method and their convergence.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

[1] Ahlberg, J. M.; Nilson, E. N.; Wash, J. L., The Theory of Splines and their Applications (1967), Academic Press: Academic Press New York · Zbl 0158.15901
[2] J. Rashidinia, Applications of splines to the numerical solution of differential equations, Ph.D. thesis, Aligarh Muslim University, Aligarh, 1994; J. Rashidinia, Applications of splines to the numerical solution of differential equations, Ph.D. thesis, Aligarh Muslim University, Aligarh, 1994
[3] Tirmizi, S. I.A., On numerical solution of third-order boundary-value problems, Commun. Appl. Numer. Math., 7, 309-313 (1991) · Zbl 0727.65069
[4] Caglar, H. N.; Caglar, S. H.; Twizell, E. H., The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions, Int. J. Comput. Math., 71, 373-381 (1999) · Zbl 0929.65048
[5] Jain, M. K., Numerical Solution of Differential Equations (1984), Wiley Eastern Ltd: Wiley Eastern Ltd New Delhi · Zbl 0536.65004
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