Overlapping grid spectral collocation approach for electrical MHD bioconvection Darcy–Forchheimer flow of a Carreau–Yasuda nanoliquid over a periodically accelerating surface

Heat Transfer ◽  
2021 ◽  
Author(s):  
M. P. Mkhatshwa
Keyword(s):  
Spectral Collocation ◽  
Collocation Approach ◽  
Forchheimer Flow

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

2021 ◽  
Vol 6 (1) ◽  
pp. 9
Author(s):  
Mohamed M. Al-Shomrani ◽  
Mohamed A. Abdelkawy
Keyword(s):  
Numerical Methods ◽  
Numerical Algorithm ◽  
Spectral Collocation ◽  
Theoretical Formulation ◽  
Numerical Examples ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Collocation Technique ◽  
Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

Vibration Analysis of Laminated and Stepped Circular Arches by a Strong Formulation Spectral Collocation Approach

2016 ◽  
Vol 08 (03) ◽  
pp. 1650036 ◽  
Author(s):  
Xiang Xie ◽  
Hui Zheng ◽  
Haosen Yang
Keyword(s):  
Boundary Conditions ◽  
Haar Wavelet ◽  
Free Vibrations ◽  
Basis Functions ◽  
Spectral Collocation ◽  
Approximation Process ◽  
Arbitrary Boundary ◽  
Collocation Approach ◽  
And Function ◽  
Strong Formulation

A strong formulation-based spectral collocation approach is presented to investigate the statics and free vibrations of laminated and stepped arches with arbitrary boundary conditions even full rings. The influences of shear deformation, inertia rotary and deepness term are considered in the theoretical model. The basic concept of the present approach is the expansion of the highest derivatives appearing in the governing equations instead of solution function itself by adopted basis functions. Then lower order derivatives and function itself are obtained by integration. The constants arising from the integrating process are determined by given boundary conditions. Due to the approximation process based on integration technique rather than conventional differentiation, it does not require the basis function to be differentiable or continuous, which makes the choice of basis functions quite freely. The robustness of the approach for the application of various basis functions is evaluated by using Haar wavelet and Chebyshev orthogonal polynomials. To test the convergence, efficiency and accuracy of the approach, the numerical results are compared with those previously published in literature. Very good agreement can be observed. A distinctive feature of the proposed approach is its unified applicability for arbitrary elastic-supported boundary conditions.

scholarly journals Jacobi Spectral Collocation Technique for Time-Fractional Inverse Heat Equations

2021 ◽  
Vol 5 (3) ◽  
pp. 115
Author(s):  
Mohamed A. Abdelkawy ◽  
Ahmed Z. M. Amin ◽  
Mohammed M. Babatin ◽  
Abeer S. Alnahdi ◽  
Mahmoud A. Zaky ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Source Term ◽  
Model Problem ◽  
Integral Form ◽  
Heat Equations ◽  
Spectral Collocation ◽  
Temperature Function ◽  
Collocation Technique ◽  
Exponential Rate Of Convergence ◽  
Collocation Approach

In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form. The proposed scheme is based on a spectral collocation approach to obtain the two independent variables. Our approach is accurate, efficient, and feasible for the model problem under consideration. The proposed Jacobi spectral collocation method yields an exponential rate of convergence with a relatively small number of degrees of freedom. Finally, a series of numerical examples are provided to demonstrate the efficiency and flexibility of the numerical scheme.

An integrated spectral collocation approach for the static and free vibration analyses of axially functionally graded nonuniform beams

2016 ◽  
Vol 231 (13) ◽  
pp. 2459-2471 ◽  
Author(s):  
Xiang Xie ◽  
Hui Zheng ◽  
Xiaoyang Zou
Keyword(s):  
Numerical Solutions ◽  
Mass Density ◽  
Variable Cross Section ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Present Approach ◽  
Variable Cross ◽  
Spectral Collocation ◽  
Section Modulus ◽  
Collocation Approach

A spectral collocation approach based on integrated polynomials is presented to investigate the statics and free vibrations of Euler–Bernoulli beams with axially variable cross section, modulus of elasticity, and mass density. The basic concept of the approach is the expansion of the highest derivatives appearing in the governing equations instead of the solution function itself by the truncated basis function. Then lower order derivatives and the function itself are obtained by integration. The constants appearing from the integrating process are determined by given classical or elastic restrained boundary conditions. Also, by incorporating the decomposition technique into the present approach, higher order vibration modes can be achieved even for stepped beams. Numerical examples including the statics and free vibrations of the beams with variance in geometry or material have been successfully solved, and the results are compared with those analytical or numerical solutions in the existing literature. The convergence and comparison studies show that convergent speed is rather rapid and the present approach can yield high accurate results with low computational efforts. Furthermore, the accuracy is not particularly affected by the adopted polynomials.

scholarly journals A Multi-Domain Spectral Collocation Approach for Solving Lane-Emden Type Equations

10.5772/63016 ◽  
2016 ◽  
Author(s):  
Sandile Sydney Motsa ◽  
Vusi Mpendulo Magagula ◽  
Sicelo Praisegod Goqo ◽  
Ibukun Sarah Oyelakin ◽  
Precious Sibanda
Keyword(s):  
Spectral Collocation ◽  
Collocation Approach

scholarly journals Accurate Spectral Collocation Computations of High Order Eigenvalues for Singular Schrödinger Equations-Revisited

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 761
Author(s):  
Călin-Ioan Gheorghiu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Error Estimation ◽  
Schrodinger Equation ◽  
Error Control ◽  
High Order ◽  
Order Of Approximation ◽  
Schrödinger Equations ◽  
Spectral Collocation ◽  
Integration Interval

In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

Sign in / Sign up

Export Citation Format

Share Document