scholarly journals Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. Sameeh ◽  
A. Elsaid
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Error Estimate ◽  
Collocation Method ◽  
Integrodifferential Equation ◽  
Chebyshev Polynomials ◽  
Difference Method ◽  
A Priori ◽  
Chebyshev Collocation Method ◽  
Partial Integrodifferential Equation

An efficient technique for solving parabolic partial integrodifferential equation is presented. This technique is based on Chebyshev polynomials and finite difference method.A priorierror estimate for the proposed technique is deduced. Some examples are presented to illustrate the validity and efficiency of the presented method.

scholarly journals Modified Chebyshev Collocation Method for Solving Differential Equations

CAUCHY ◽  
2015 ◽  
Vol 3 (4) ◽  
pp. 208
Author(s):  
M Ziaul Arif ◽  
Ahmad Kamsyakawuni ◽  
Ikhsanul Halikin
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Collocation Method ◽  
Difference Method ◽  
Numerical Scheme ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Polynomial Collocation

This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial) collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial) collocation method is applied to both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

BLOOD FLOW THROUGH A CIRCULAR PIPE WITH AN IMPULSIVE PRESSURE GRADIENT

2000 ◽  
Vol 10 (02) ◽  
pp. 187-202 ◽  
Author(s):  
GIUSEPPE PONTRELLI
Keyword(s):  
Blood Flow ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Unsteady Flow ◽  
Pressure Gradient ◽  
Collocation Method ◽  
Difference Method ◽  
Flow Through ◽  
Impulsive Pressure

The unsteady flow of a viscoelastic fluid in a straight, long, rigid pipe, driven by a suddenly imposed pressure gradient is studied. The used model is the Oldroyd-B fluid modified with the use of a nonconstant viscosity, which includes the effect of the shear-thinning of many fluids. The main application considered is in blood flow. Two coupled nonlinear equations are solved by a spectral collocation method in space and the implicit trapezoidal finite difference method in time. The presented results show the role of the non-Newtonian terms in unsteady phenomena.

Multidomain Chebyshev spectral method for 3-D dc resistivity modeling

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1616-1623 ◽  
Author(s):  
Shengkai Zhao ◽  
Matthew J. Yedlin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Spectral Method ◽  
Direct Current ◽  
Chebyshev Polynomials ◽  
Difference Method ◽  
Dc Resistivity ◽  
Chebyshev Spectral Method ◽  
The Finite Difference Method ◽  
Resistivity Modeling

We use the multidomain Chebyshev spectral method to solve the 3-D forward direct current (dc) resistivity problem. We divided the whole domain into a number of subdomains and approximate the potential function by a separate set of Chebyshev polynomials in each subdomain. At an interface point, we require that both the potential and the flux be continuous. Numerical results show that for the same accuracy the multidomain Chebyshev spectral method is 2 to 260 times faster than the finite‐difference method.

A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation

2018 ◽  
Vol 11 (08) ◽  
pp. 1850099 ◽  
Author(s):  
Mohamed M. Khader ◽  
Khaled M. Saad
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Collocation Method ◽  
Numerical Study ◽  
Fisher Equation ◽  
Chebyshev Collocation Method ◽  
The Third ◽  
The Finite Difference Method

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

Modelling of a desiccant rotor by using the collocation method

2013 ◽  
Vol 24 (1) ◽  
pp. 201-220 ◽  
Author(s):  
Marcello Aprile ◽  
Mario Motta
Keyword(s):  
Mass Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Heat And Mass Transfer ◽  
Collocation Method ◽  
Difference Method ◽  
Transfer Problem ◽  
Operating Conditions ◽  
Content Type ◽  
The Finite Difference Method

Purpose – This article aims to develop a fast numerical method for solving the one-dimensional heat and mass transfer problem within a desiccant rotor. Design/methodology/approach – The collocation method is used for discretizing the axial dimension and reducing the number of dependent variables. The resulting system of equation is then solved through backward differentiation formulas. Findings – The numerical results obtained here focus on verifying the accuracy and the computation time of the proposed method with respect to the finite difference method. The proposed numerical solution method resulted faster than, and as much accurate as, the finite difference method, over a large range of operating conditions that are of interest in desiccant cooling applications. Research limitations/implications – For heat and mass transfer analysis, constant average transfer coefficients are used. The results are calculated for NTU between 2 and 15 and for Le number between 0.5 and 2. Practical implications – The results can be used in designing desiccant heat exchangers and desiccant cooling systems including complex rotor arrangements. Originality/value – Different from other simplified solution techniques, the proposed method relies on few parameters that retain physical meaning and applies also to complex rotor configurations.

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