This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show ...

ÐThe unsteady ̄ow of blood in a straight, long, rigid pipe, driven by an oscillatory pressure gradient is studied. Three di€erent non±newtonian models for blood are considered and compared. One of them turns out to o€er the best ®t of experimental data, when the rheological parameters are suitably ®xed. Numerical results are obtained by a spectral collocation method in space and the implicit tr...

Pseudospectral collocation is employed for the numerical solution of nonlinear two-point boundary value problems with separated end conditions. Second-order finite difference schemes are used as preconditioners for the spectral calculation, and a solution of the discretized equations is obtained using versions of the defect correction principle. The method and a variant based on an adaptive gri...

Similarity solutions for the flow of granular materials are constructed. Unlike previous work, the present approach can be applied to non-axisymmetric containers. The steady state equations are reduced to a nonlinear Helmholtz on a subdomain of the sphere. Existence and local uniqueness of the solutions are established. A spectral numerical method using Fourier/ChebyshevGauss-Radau collocation ...

Stable and accurate surface-wave calculations present a long-standing numerical and analytical challenge to seismologists. In a layered medium, we can describe the surface-wave behavior with harmonic time dependence in terms of an eigenproblem where the eigenvalues and eigenfunctions define the surface-wave modes. Numerous studies have explored diverse numerical approaches to solve this eigenpr...

A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacia...