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**Spectral shifted Jacobi tau and collocation methods for solving fifth-order boundary value problems.**
*(English)*
Zbl 1221.65171

Summary: We present an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs). An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34B05 | Linear boundary value problems for ordinary differential equations |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

### Keywords:

spectral algorithm; Jacobi tau method; linear fifth-order two-point boundary value problems; Jacobi collocation technique; numerical examples### Software:

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\textit{A. H. Bhrawy} et al., Abstr. Appl. Anal. 2011, Article ID 823273, 14 p. (2011; Zbl 1221.65171)

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### References:

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