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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 Boundary value problems for ODE (numerical methods) 34B15 Nonlinear boundary value problems for ODE 65L20 Stability and convergence of numerical methods for ODE
Full Text:
References:
 [1] Ahlberg, J. M.; Nilson, E. N.; Wash, J. L.: The theory of splines and their applications. (1967) · Zbl 0158.15901 [2] 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) · Zbl 0536.65004