Troesch's problem: A B-spline collocation approach

Mathematical and Computer Modelling

Volumn 54, Issue 9-10, 2011, Pages 1907-1918

  Khuri, S A ^a   Sayfy, A ^a  

^a AMERICAN UNIVERSITY OF SHARJAH   (United Arab Emirates)

Author keywords

B splines; Boundary values problems; Collocation; Shishkin type mesh; Troesch's problem

Indexed keywords

B SPLINES; BOUNDARY VALUES; COLLOCATION; SHISHKIN-TYPE MESH; TROESCH'S PROBLEM;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; NEWTON-RAPHSON METHOD; SHIP PROPELLERS;

SPLINES;

EID: 80051583591     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.04.030     Document Type: Article

References (17)

1. Weibel E.S. The Plasma in Magnetic Field 1958, Stanford University Press, Stanford. R.K.M. Landshoff (Ed.).
2. Roberts S.M., Shipman J.S. On the closed form solution of Troesch's problem. Journal of Computational Physics 1976, 21:291.
3. Feng X., Mei L., He G. An efficient algorithm for solving Troesch's problem. Applied Mathematics and Computation 2007, 189:500-507.
4. Khuri S.A. A numerical algorithm for solving the Troesch's problem. International Journal of Computer Mathematics 2003, 80(4):493-498.
5. Scott M.R. On the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms. Numerical Solutions of Boundary-Value Problems for Ordinary Differential Equations 1975, 89-146. Academic Press, New York. A.K. Aziz (Ed.).
6. Chang S.H., Chang I.L. A new algorithm for calculating the one-dimensional differential transform of nonlinear functions. Applied Mathematics and Computation 2008, 195:799-808.
7. Chang Shih-Hsiang A variational iteration method for solving Troesch's problem. Journal of Computational and Applied Mathematics 2010, 234:3043-3047.
8. Bahadir A.R. Application of cubic B-spline finite element technique to the thermistor problem. Applied Mathematics and Computation 2004, 149:379-387.
9. Caglar H.N., Caglar S.H., Twizell E.H. The numerical solution of third-order boundary value problems with fourth-degree & B-spline functions. International Journal of Computer Mathematics 1999, 71:373-381.
10. Caglar H.N., Caglar S.H., Twizell E.H. The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions. Applied Mathematics Letters 1999, 12:25-30.
11. Deeba E., Khuri S.A. Nonlinear Equations. Wiley Encyclopedia of Electrical and Electronics Engineering 1999, vol. 14:562-570. John Wiley & Sons, New York.
12. Luigi Brugnano, Francesca Mazzia, Donato Trigiante, Fifty years of stiffness. [math.NA] (20.10.09). arxiv:0910.3780v1.
13. Ahlberg J.H., Ito T. A collocation method for two-point boundary value problems. Mathematics of Computation 1975, 29(131):761-776.
14. Farrell P.A., Hegarty A.F., Miller J.J.H., O'Riordan E., Shishkin G.I. Robust Computational Techniques for Boundary Layers 2000, Chapman and Hall, CRC Press.
15. Miller J.J.H., O'Riordan E., Shishkin G.I. Fitted Numerical Methods for Singular Perturbation Problems 1996, Word Scientific, Singapore.
16. Carey G.F., Dinh H.T. Grading functions and mesh redistribution. SIAM Journal on Numerical Analysis 1985, 22(5):1028-1040.
17. Christara C.C., Ng Kit Sun Adaptive techniques for spline collocation. Computing 2006, 76:259-277.