## THERMAL SCIENCE

International Scientific Journal

### THE BARYCENTRIC RATIONAL INTERPOLATION COLLOCATION METHOD FOR BOUNDARY VALUE PROBLEMS

**ABSTRACT**

Higher-order boundary value problems have been widely studied in thermal science, though there are some analytical methods available for such problems, the barycentric rational interpolation collocation method is proved in this paper to be the most effective as shown in three examples.

**KEYWORDS**

PAPER SUBMITTED: 2017-10-01

PAPER REVISED: 2017-12-12

PAPER ACCEPTED: 2017-12-12

PUBLISHED ONLINE: 2018-09-10

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**4**, PAGES [1773 - 1779]

- Noor, M. A., Variational Iteration Technique for Solving Higher Order Boundary Value Problems, Ap-plied Mathematics and Computation, 189 (2007), 2, pp. 1929-1942
- Wazwaz, A. M., The Numerical Solution of Fifth-Order Boundary Value Problems by the Decomposi-tion Method, Journal of Computational and Applied Mathematics, 136 (2001), 1, pp. 259-270
- Zhang, J., The Numerical Solution of Fifth-Order Boundary Value Problems by the Variational Iteration Method, Computers and Mathematics with Applications, 58 (2009), 11, pp. 2347-2350
- Mestrovic, M., The Modified Decomposition Method for Eighth-Order Boundary Value Problems, Ap-plied Mathematics and computation, 188 (2007), 2, pp. 1437-1444
- Sablonniere, P., Univariate Spline Quasi-Interpolants and Applications to Numerical Analysis, Rendi-conti del Seminario Matematico, 63 (2005), Apr., pp. 211-222
- Berrut, J. P., Barycentric Lagrange Interpolation, SIAM Review, 46 (2004), 3, pp. 501-517
- Berrut, J. P., Rational Functions for Guaranteed and Experimentally Well-Conditioned Global Interpola-tion, Computers and Mathematics with Application, 15 (1988), 1, pp. 1-16
- Berrut, J. P., Barycentric Formulae for some Optimal Rational Approximants Involving Blaschke Prod-ucts, Computers and Mathematics with Application, 44 (1990), 1, pp. 69-82
- Berrut, J. P., The Barycentric Weights of Rational Interpolation with Prescribed Poles, Journal of Com-putational and Applied Mathematics, 28 (1997), 1, pp. 45-52
- Liu, H. Y, et al., Barycentric Interpolation Collocation Methods for Solving Linear and Nonlinear High-dimensional Fredholm Integral Equations, Journal of Computational and Applied Mathematics, 327 (2018), Jan., pp. 141-154
- Luo,W. H., et al. Barycentric Rational Collocation Methods for a Class of Nonlinear Parabolic Partial Differential Equations, Applied Mathematics Letters, 68 (2017), June, pp. 13-19